Is it permissible for me to visit my relative who is a murderer in prison?

Maintaining kinship ties (Silat al-Rahim) is obligatory according to the Qur'an, the Sunnah (definition), and the consensus of the scholars. As for maintaining ties with or shunning a transgressor (fasiq), this is subject to what serves the greater interest. If visiting him will reform him and benefit him in his religion, then you should visit him and advise him. However, if shunning him is more beneficial for his condition, then that is the preferred course of action.