You can attempt to do it, but I wouldn't recommend it.
The 9600GT uses about 61w of power on 12v rail under typical gaming conditions. That works out to just a bit over 5 amps. The CPU, fans, hard drives and optical drives also draws power from the 12v rail as well. While it may be fine in the short term, the more you max out your PSU the sooner it is likely to fail.
When your PSU fails and you are lucky, then all you need to do is replace the PSU. If you are unlucky, then at least one other component in your PC can be damaged. Trying to find it (them) can be tricky. If you are really unlucky, then you will need to replace your entire PC.
The question is, how lucky do you feel?
Based on a 230w PSU, my recommendation is the Radeon HD 5570 which uses about 19w of power under normal gaming conditions.
If you want to use the 9600GT, then I would get at least a 350w PSU from a reliable name brand like Antec, Enermax, FSP, Corsair, PC Power & Cooling, Seasonic, OCZ, and XFX just to name a few.