Within the movie version of The Two Towers Saruman created Uruk-hai in the pits below Orthanc that were willing to kill Mordor orcs when the orcs attempted to harm the hobbits.
Could Gandalf (or another free leader) have created orcs to be used against Sauron?
I have no source for this (it is a speculative question) but I don't see why not.
If Saruman could do it, Gandalf probably could have too. However, for this to happen Gandalf would need to become fundamentally corrupted in some way and in many senses would no longer be Gandalf as we know him. His army would be challenging Mordor for the purposes of gaining his own power, not for the defence of the free peoples of Middle-earth.
Based on the question as asked by the OP, I'm assuming that the question is "Is it possible that Gandalf was the being who created the Orcs?" (See below for an answer to the other interpretation, "Could Gandalf have created his own Orcs to use against Sauron?")
Definitely not:
(1) The orcs are mentioned numerous times in The Silmarillion, which predates Gandalf's arrival in Middle-earth.
(2) Additionally, The Silmarillion reports that the Wise all believed that the Orcs were made by Morgoth:
But of those unhappy ones [lost Elves] who were ensnared by Melkor little is known of a certainty. For who of the living has descended into the pits of Utumno, or has explored the darkness of the counsels of Melkor? Yet this is held true by the wise of Eressëa, that all those of the Quendi who came into the hands of Melkor, ere Utumno was broken, were put there in prison, and by slow arts of cruelty were corrupted and enslaved; and thus did Melkor breed the hideous race of the Orcs in envy and mockery of the Elves, of whom they were afterwards the bitterest foes. For the Orcs had life and multiplied after the manner of the Children of Ilúvatar; and naught that had life of its own, nor the semblance of life, could ever Melkor make since his rebellion in the Ainulindalë before the Beginning: so say the wise. And deep in their dark hearts the Orcs loathed the Master whom they served in fear, the maker only of their misery.
Added: OK, the other interpretation "Could Gandalf have created his own Orcs to use against Sauron?" Has the answer, "Probably yes if he wanted to and spent enough time and effort learning the process. But he couldn't have done it without also going rogue."
It was not in Gandalf's personality. In Valinor, he was known as Olórin and
Wisest of the Maiar was Olórin. He too dwelt in Lórien, but his ways took him often to the house of Nienna, and of her he learned pity and patience.
But of Olórin that tale does not speak; for though he loved the Elves, he walked among them unseen, or in form as one of them, and they did not know whence came the fair visions or the promptings of wisdom that he put into their hearts. In later days he was the friend of all the Children of Ilúvatar, and took pity on their sorrows; and those who listened to him awoke from despair and put away the imaginations of darkness.
...
[Gandalf] would have no ties and no allegiance, save to those who sent him, and he would abide in no place nor be subject to any summons.
None of this shows the kind of person who would created a race of perverted monsters to fight Sauron.
Also, fighting Sauron directly was not his mandate, since
[Gandalf was a messenger] sent by the Lords of the West to contest the power of Sauron, if he should arise again, and to move Elves and Men and all living things of good will to valiant deeds.
