First, it is ridiculous to ask if a PSU will work with X video card when you don't mention the rest of the system.
Second, it is ridiculous for others to suggest it will (or won't) until they KNOW what else you are powering with Z power supply.
However, having written this much a 7600GS is a very power miserly video card, in most cases if your system had ample reserve power it would not be necessary to upgrade the PSU to use one. Problem is we lack enough info to know if you have ample reserve power.
Since OEM PSU are generally rated far far far better than the typical retail PSU, you should probably ignore anyone trying to relate the rated current of yours to some retail PSU because that is an apples ranges comparison. In general OEM PSU are rated similar to how PC Power & Cooling rates, for sustainable output at higher temp, not peak power at 25C. This is the case because OEMs have real engineers that catch lies and need viable lifespans from systems while retail channels can pull a lot of stunts a quick web review won't catch.
In summary, it is about the most performance per watt you could hope for, if an efficient video card is the goal then it is the best bet. You make no mention of whether your PSU is std. or proprietary though, if standard it wouldn't be an extreme expense to upgrade that later, but your present PSU should suffice for the time being, ASSUMING you don't have a very large draw off the 12V rail (more than a typical system starting with 300W PSU would have).
Do you guys still think itd be fine to get the 7600GS, with my PSU, or is there any other options for other cards?
I know the 7600GS doesnt draw that much power.
Does it matter if the 7600GS has a fan or not? Because i would guess it would draw more power if it had a fan, but this one is fanless. If that helps in anyway lol.
Suppose your CPU has a peak TDP of 120W (I'm too lazy to look it up but you can if you're right at the border). Typical motherboard CPU VRM subcircuit is about 93% efficient. So for entire CPU+power delivery we have a peak, not typical, power consumption of;
(120/0.93) = 129W
129W / 12V = ~ 11A
Now add to that the currents of other power consumers. Suppose 1A for fans (it'd not likely that high on an OEM system even including video card fan but it's a nice round number even if rounding off, "0A" is probably closer.
Now add the HDD and optical and let's pretend both are at max peak power consumption (which is impossible since that would be when HDD spins up at POST and at that point you can't be already reading an optical disc).
Now 7600GS peaks around 27W and IIRC it is not all 12V power but for this example let's assume it is.
27 / 12 = 2.25A
11A CPU + 1A fans + 2.4A drives + 2.25A video = 16.7A
With a low-end generic or some branded retain PSU you might need a unit rated for more than 17A, but with a typical major OEM PSU if it were rated for 17A you could expect it can deliver that.
We haven't even addressed that it would be exceptionally hard (impossible) to run the system in a state with peak 3D gaming, peak CPU, peak HDD spinup and reading an optical drive all simultaneously. Typical current for this system would probably be closer to 12A @ 12V. IOW, a PSU actually rated for about 14A of 12V current but high peak currents (Sparkle, PC Power & Cooling, etc do this) would run the system so long as it wasn't a very old PSU design meant for past eras that used a highly weighted 5V voltage reading to regulate, which could tend to make the 12V voltage sag some.
In short, unless the PSU is dishonestly rated, there is no reasonable goal of 20A 12V power. It would be an arbitrary overkill even with this "supposed" high power CPU. Details matter. However, overkill is not so bad, a margin of operating below peak output can be desirable but it should be seen more as a choice when buying a new PSU, rather than a reason to disqualify use of the existing PSU.