Will this card run a game like SWTOR run smoothly on low to medium settings?
No it won't. That's basically one of the absolute weakest graphics cards out there right now. It can't even run Skyrim at the lowest settings above 10 fps, presumably at a resolution of 1280x720. It'll be near impossible to do any gaming with that, and I'm not even sure how it'd fair with very casual gaming.
I assume that's a notebook, so my recommendation is to get a new laptop entirely.
The Radeon HD 7310 is a pretty weak graphics core in a pretty weak AMD E1-1200 APU released last year. The E1-1200 APU is basically a E-300 APU with a 100MHz increase in clockspeed for the CPU core. The Radeon HD 7310 is just a minor update of the Radeon HD 6310.
Those APUs are meant for netbooks. You can check out some Youtube gameplay videos in the following link where the poster plays some games with the Radeon HD 7310.