Nope, 13” is iGPU (part of the CPU). However even in the models with a dGPU, you can’t upgrade the graphics as they’re part of the Logic Board.
Tbh there are very few laptops with upgradable graphics cards, unless they’re gaming laptops.
The best you can do to increase GPU performance is max the RAM to 16GB as this will increase VRAM, but this won’t enable compatibility with an unsupported OS and the performance difference for games would be negliable, if non-existent.
It’s a case of a new computer I’m afraid if you’re looking to run the latest OS to a good standard. You can pick up a 2012 13” for far cheaper than a 2011 13” used due to market saturation with the length of time they sold it. Plus this boasts USB 3, a better CPU, better GPU, faster RAM, and is likely to be supported by Apple until 2021 due to 5-6 years EOL from last sold.
In a perfect world I’d recommend saving for a 2015 or higher as this will be a vastly better spec jump and they have much better build quality — the cMBP 13” suffered from high failure rate on the SATA cables.
Sorry for the long post and please let me know if there’s anything I can clarify.