You have to have bird rights in order to sign someone over your salary cap. So it would have to be a player who was on your team the year before who was eligible for the Bird exception.
"In essence, the Larry Bird exception allows teams to exceed the salary cap to re-sign their own free agents, at an amount up to the maximum salary. To qualify as a Bird free agent, a player must have played three seasons without being waived or changing teams as a free agent. Players claimed after being amnestied have their Bird rights transferred to their new team."
http://en.wikipedia.org/wiki/NBA_salary_cap
If you don't have Bird rights then you cant go over the cap to sign him.