Will radio stations let me sing?

I have always enjoyed the singing of Frank Sinatra, Bing Crosby, and many other great crooners. I was recently told that I have a beautiful voice by the jazz instructor here at CSU in Columbus, GA, but also told that any male vocalist part most likely would not come my way because I am not a music major. Will radio stations allow me to sing on them to get the exposure I need to be heard? If so, how can I go about setting this up?