Is Leia considered a Jedi? She does have the Force but she doesn't have a lightsaber, nor did she undergo training like Luke. What are the requirements in order to be called a Jedi?
Is Leia considered a Jedi?
No. She is Force-sensitive but not trained.
The new canon novel Bloodline gave us a bit more information about Leia and the Force. She chose to remain involved in Republic politics. She is aware of the Force, and occasionally able to use it in extremis. From Bloodline:
"I think some Centrist senators might just be taking kickbacks in return for hiding what looks like the biggest drug cartel of the past twenty years." [Greer said]
But the princess shook her head no. "That's not what I sense."
Joph frowned. Sense? What did that have to do with anything? He knew better than to ask out loud.
Later in the novel:
The others evacuating flooded through the doors behind and around her, but once they were clear of the structure, half of them stopped, remaining stupidly within range.
Within range of what? She still didn't know. But every instinct within her - the Force itself - screamed that disaster was near.
She's also aware that she used the Dark Side when she killed Jabba in Episode VI. While she watches a recording of the event:
With a kind of awe, Leia watched herself sling the heavy chains around Jabba's neck. The sheer strength it took to compress a Hutt's neck to the point of asphyxiation - she had summoned that from somewhere deep inside, remembered doing so, but found it almost unbelievable to witness. Pure hatred had fueled her. Her arms seemed to ache with remembered strain.
The terminology here is pretty clear - the strength needed to strangle a Hutt is normally beyond a mere human, but she succeeded...and she did so using the power of her hatred. That's textbook Dark Side. Now yes, it's true that humans are capable of pushing themselves much harder in extreme circumstances than we might ever expect, but in this case we have:
A known Force sensitive individual, who
Drew on her anger to...
Enhance her strength and...
Perform a super-human feat.
Hutts may look like sedentary blobs of fat, but they're a lot stronger than they look. The death of Jabba was rare enough that some species know Leia by the name "Huttslayer". Hutts were hard to kill; Leia made it look easy. What does that tell you?
What are the requirements in order to be called a Jedi?
"Jedi" is not simply a description of a person who uses the Force; it's the title given to members of the Jedi Order. We don't know for sure what criteria there were for membership in the new Jedi order that Luke tried to build; in the old Jedi order that he was trying to emulate, a Jedi was a person who was trained and governed by the Jedi Order.
Even those who were trained by the Jedi but left the Order were not considered Jedi; Ahsoka Tano, former apprentice of Anakin Skywalker, was cast out of the Jedi order, and then refused to return when her name was cleared. Even when it was offered to her, she refused the title of Jedi; she was not part of the Order, so she was no Jedi.
"Jedi" could then be seen as something like "Marine" - not everyone who carries a rifle is a Marine; not everyone who can touch the Force is a Jedi.
In order to be called a Jedi, one has to be rigorously trained since childhood. Leia was not trained in the movies, making her a mere Force-sensitive person. Also, the Jedi order did no longer exist during episodes IV to VI.
If you accept an answer involving other media, then Leia may be a bit Jedi-ish in an add-on for Star Wars: The Force Unleashed II. There, (spoilers!)
No. She had no master and was never trained to use the Force. She was never awarded that title. Luke had to fight Vader (twice) before he earned that title (Yoda: "No more training do you require. Already know you that which you need" Luke: "Then I am a Jedi". Yoda: "Not yet... ... you must confront Darth Vader again, then, only then, a Jedi will you be."
Anakin was also very strong with the force when he was young, but it didn't make him a Jedi: Obi-Wan (speaking to Luke): "Anakin was a good friend. When I first knew him, your father was already a great pilot. But I was amazed how strongly the Force was with him. I took it upon myself to train him as a Jedi. I thought that I could instruct him just as well as Yoda."
Also - there is this: Yoda (speaking to Luke): "When gone am I, the last of the Jedi, will you be." Leia did no force training after that.
By the end of the Dark Nest trilogy, Leia's master Saba Sebatyne classed her as a fully fledged Jedi knight.
She also had training from Luke, Callista, Mara Jade and Vima Boda in various (legends) EU novels.