Looking at the case it is in i would save no. you might be able to fit a very small no so powerful card in there. If you want a gameing right consider looking the deals section of the forum you might find a cheap custom PC there that will fit you needs.
Edit: pre-assembled computers like these, rarely have the room to fit in a add on card, they are ment to be casual computers, word docs, internet, and maybe some media, nothing flashy.