I wouldn't. I believe the 7950GT requirement is somewhere around 400W. Usually 250W PSU's aren't used for much more than a system with integrated graphics. You might be able to get by with an HD5570 which would would outperform the 7950GT anyways.
As budget PSUs age they loose their ability to output the full rated power.
Your 250W PSU is unlikely to be able to support a GT 7950 if it's actually three years old.