We need to know more about your system. A CPU upgrade might help if your currrent CPU is too slow for that game. However we need to know which graphics card you have and how much RAM you have. A very weak graphics card or too little RAM can also cause poor gaming performance.
Lucky for you, I happen to have some experience with SWTOR in a variety of configurations.
First configuration was an E6600 (65nm) @ 3.0 GHz paired up with an HD 4870. I didn't overclock the GPU, and got barely playable framerates at medium settings. Turning off shadows helped immensely, and the game was perfectly playable, but didn't look great.
Next configuration was an E6700 (65nm) @ 3.2 GHz paired with the same HD 4870. I didn't notice a difference in performance.
Next I replaced the 4870 with a 6950, and cranked the core clock up from 800 MHz to 960 MHz. I went from 20-40 FPS on medium settings to 60-100 FPS with everything maxed out. Still not smooth, though. The game froze for a fraction of a second every time I summoned my companion or dismounted my speeder.
Finally, I swapped out the E6700 for a Xeon X3210. The Xeon is quad core, but clocked very low, so I cranked it up to 3.5 GHz. I no longer get stuttering, and my framerates don't take nearly so many dives in highly populated areas. I never drop below 100 FPS in space combat.
So, my personal recommendation is this:
1. Get a quad core CPU. You can find the X3210 or X3220 on eBay for next to nothing these days, but they need serious overclocking to be worth it due to their very low stock speeds.
2. Any mid-high end video card from the last two years will give you playable framerates. The 6870 is probably more than enough for the game, or whatever the Nvidia equivalent is.
3. Surprisingly, an SSD doesn't improve load times. The game is just really inefficient right now.