Answering this question, Dr. `Abd al-Fattah Idris, professor of Islamic jurisprudence in Al-Azhar University, said,

No, he is absolutely not allowed to do this because what is permissible for a man is to look to the woman he is willing to marry, but it is not permissible to touch anything of her body. So, in this case a woman or a mahram (non-marriageable male relative) may put the ring in her finger on his behalf.