It appears that "subject," as in the kind for an experiment or research is called 被験者（ひけんしゃ）in Japanese. So you might say: 被験者になってくれませんか？ I must say though, that the need for such a phrase is rather unlikely. XD

"Subject" has another meanings. In the case of art, Japanese use "モデル". So you can say: 私の絵の(or写真の)モデルになってくれませんか？

It's a bit difficult to answer this question without more context. Please provide an English dictionary definition of subject (there's many meanings) and then someone may be able to help you.