In Return of the Jedi, we learn that Leia is Force-sensitive, which is somewhat second to all her other heroic qualities, but still a nice touch. However, it appears that the intervening 30 years have not seen her pick up the lightsaber and robes. And she has a good reason, it turns out, for not doing so.
IGN asked J.J. Abrams about it, and he replied that basically Leia’s just been too busy trying to free the galaxy to goof around with a laser sword:
…it was simply a choice that she made, that her decision to run the Rebellion, and ultimately this Resistance, and consider herself a General, as opposed to a Jedi. It was simply a choice that she took.
We already know the Empire didn’t exactly go away after the second Death Star was blown up, and it seems that she was too busy trying to free the galaxy to learn about an ancient order of space wizards. That said, though, Abrams notes her ability to use the Force is, in his words, “an intrinsic piece of her character” and it seems unlikely such a plot thread would just be unceremoniously dropped. But we’ll find out December 18.