Sauron created The One Ring to gain control over the other ring-bearers, but it also amplified his power. Since it's a bad idea for anyone to claim The One Ring, wouldn't it be possible for Gandalf to create his own One Ring?
In the foreword to The Lord of the Rings, Tolkien observes:
Saruman, failing to get possession of the Ring, would in the confusion and treacheries of the time have found in Mordor the missing links in his own researches into Ring-lore, and before long he would have made a Great Ring of his own with which to challenge the self-styled Ruler of Middle-earth.
Tolkien therefore definitely conceives of Saruman as being capable of making a Ring, and therefore Gandalf would presumably have been likewise capable.
However, what we can also take from that statement is that making a Ring is not a simple task; there is some "lore" involved, and we know from elsewhere that Saruman had made especial study of the Rings of Power, but yet Tolkien states that even he would have required knowledge found only in Mordor to complete his own work.
So, to summarise:
- Yes, but,
- It's neither quick nor easy, because,
- There is considerable "lore" involved, and,
- It requires hundreds or even thousands of years of dedicated study to get to a "Saruman-level" of "lore", and,
- Even then there will be missing knowledge which may only be found in Mordor.
- So for all practical purposes it's actually "No".
I doubt it.
Going through all the artifacts throughout the books, the knowledge of forging great magical artifacts seems to mainly originate from the Vala Aulë.
- Sauron (and Saruman) was originally a Maia of Aulë.
- The greatest craftsman through the ages, Fëanor, was a student of Aulë.
- The knowledge of making the elven rings came from Annatar/Sauron. But knowledge was likely also passed down from Fëanor, to his son Curufin, to his son Celebrimbor.
The recurring pattern in the making of almost all magical artifacts in the books, is great smithing skill.
Sauron, Fëanor and Celebrimbor were all skilled mastersmiths. The most powerful artifacts of Middle-Earth through the ages were made by these three. When it comes to the creation of magical items, craft in smithing seems to be an important skill, perhaps more so than knowledge of magic and lore.
There is no indication throughout the books that Gandalf, or anyone else but the mentioned three characters would have the ability to forge major magical artifacts like the Silmarils, the Palantíri or the Rings of Power. Even the Phial of Galadriel originates from Fëanor, as all Galadriel did was to capture the light of a Silmaril.
No elves outside the House of Fëanor attempt to make major artifacts. Neither does anyone of the other races, save for Sauron. Minor magical aritfacts like the swords Anglachel or Glamdring can evidently be made by other skilled smiths.
The necklace Nauglamír was made by dwarves - the children of Aulë and skilled smiths - but it doesn't seem to have any magical abilities beyond beauty. Similarly, dwarven items made of Mithril seem to be both beautiful and of extra-ordinary high quality, but not necessarily magical.
The rings made by Sauron, and specifically the One Ring, did not give Sauron extra raw power, they were a method of applying his existing, innate power over men, dwarves and elves. The rings did not amplify Sauron's power, they attempted to apply it more effectively. (This did not work completely as intended on the dwarves and elves of course, and it enabled Sauron to eventually be destroyed).
Sauron put a lot of himself and his power into the rings. You could almost say the rings were a part of Sauron. The rings are 'of power' because they give the wearer some of Sauron's power.
If Saruman could make similar rings he would have used them in the same way - to attempt to control his own men and orcs.
If Gandalf made a ring or rings, he would not be any more powerful in total, as he'd have to put his own power into them. If he did make rings, the effect on a wearer would probably just be to make them like hobbits a bit more.
It's rather like building your own computer. You may know the theory, but you really need a certain industrial base to support a silicon fab plant. So Gandalf might know how a Ring is made, but he can't just wish it into being. He (or anyone) needs all that supporting infrastructure that really doesn't exist in the Third Age.
The more interesting question, now that I think on it, is why Sauron didn't make more rings. Even if they're not nearly as powerful as the One Ring, they'd still be useful. He seems to have the industrial base in Mordor, and is said to still use the fires of the Sammath Naur on occasion...
There are a lot of great answers already, and I would elaborate a bit on VictimOfCircumstance's suggestion of time being an issue.
By the time the Istari (wizards) were dispatched to Middle-earth, Sauron was already extremely powerful, not to mention a master smith on the level of (if not more skilled than) Celebrimbor. For Gandalf (or Saruman for that matter) to learn the magical lore as well as the smithing skill required to forge a ring equal to the One, it would likely have taken more time than they had. This is suggested by the fact that it took Sauron quite a while to accomplish the feat, even though he had served Aulë, the great smith, before he was corrupted by the evils of Morgoth.
In addition to that, there are moral considerations. Gandalf already bore one of the 3 elven rings, and would therefore have been acutely aware of the effects of even the most benign of the rings of power. He also knew that the old adage "absolute power corrupts absolutely" was especially true when it comes to magic. He had served Manwë, and was said to be the wisest of the Maiar, while he lived in Valinor. When he was asked to be among the Istari sent to Middle-earth he did not want to go, saying that he feared Sauron and lacked the strength to challenge him. Manwë's response was that this was more reason for him to go, and Gandalf likely understood this to mean that he would need to unite the peoples of Middle-earth to accomplish his goal. He would therefore be wary of any path to success that focused on increasing his own power instead of increasing the cooperation and wisdom of the mortals he was there to help.
There are two aspects of the One Ring.
- It is a ring of power
- It Rules Them All (the 9, the 7, and the 3)
The other answers address Gandalf making a ring of power in general.
The thing that makes the One special is that it rules them all, and this is because Sauron helped the elves, dwarves, and men make their rings of power and made the One simultaneously in secret to control them. A new ring of power made much later by someone else probably could not be another "One Ring" in this respect.