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 Star Wars: The Force Unleashed II. There,

the dark clone of Galen Marek goes off to kill Leia on Endor, where she fights him (quite skillfully), using the Force, her lightsaber, and stuff

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!)

the dark clone of Galen Marek goes off to kill Leia on Endor, where she fights him (quite skillfully), using the Force, her lightsaber, and some other stuff

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 Star Wars: The Force Unleashed II. There,

the dark clone of Galen Marek goes off to kill Leia on Endor, where she fights him (quite skillfully), using the Force, her lightsaber, and stuff

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 Star Wars: The Force Unleashed II. There,

the dark clone of Galen Marek goes off to kill Leia on Endor, where she fights him (quite skillfully), using the Force, her lightsaber, and stuff