Manrique was born in Barranquilla, Colombia and earned a B.A. from the University of South Florida.

His first poetry volume won Colombia's National Poetry Award. Additionally, he received a Guggenheim Fellowship to write his memoirs and has contributed to Shade (1996), a gay, black fiction anthology. He has also produced the non-fictional book, Eminent Maricones which explores the works of Reinaldo Arenas, Manuel Puig, and Federico García Lorca. In 1999 he was awarded a grant from the Foundation for Contemporary Arts Grants to Artists Award.

He has taught creative writing at Mount Holyoke College, New York University, and The New School for Social Research. He is currently a professor in the M.F.A. program at Columbia University.