No, not the TIE/LN fighter (commonly known as the "TIE fighter") or TIE/IN Interceptor ("TIE Interceptor").
In Episode IV, the Millenium Falcon comes out of hyperspace and encounters a TIE fighter from the Death Star. Obi-Wan says it's a "short range fighter" and "a fighter that size couldn't get this deep into space on its own":
Luke: It followed us!
Ben: No. It's a short range fighter.
Han: There aren't any bases around here. Where did it come from?
Ben: A fighter that size couldn't get this deep into space on its own.
The (Legends) Wookieepedia article for the TIE fighter also explicitly says it lacks a hyperdrive.
However, certain advanced or upgraded models -- such as the TIE Advanced x1 used by Darth Vader at the Battle of Yavin -- did include a hyperdrive.