You might not even think of Tai Chi as a martial art, and that's because although Tai Chi is in fact a martial art, it is also something of a meditative practice akin to yoga. Similar to the aikido suggestions below, Tai Chi is not a striking art, but is mostly about redirecting the opponent's energy, as well as moves that hinder or disable the opponent from attacking you in the first place. Tai Chi focuses on sensitivity and receptiveness rather than force or strength, so even if you do it for years, you won't come out of it looking like Bruce Lee, which may or may not be a positive for you.
I don't have a lot of experience with other martial arts, aside from a few random Karate lessons when I was young, but I've been going to a local Tai Chi class for about 6 months now and I highly recommend it.