In 1975, he auditioned with Pedro Conga and his International Orchestra and was hired as a singer. After a short while, he left the band and joined the "Conjunto Borincuba", conducted by Justo Betancourt, as lead singer. With this band, he participated in the recording of Con Amor (With Love), which became a "hit" in 1978.

That same year Rojas joined the Fania All-Stars and had a "hit" song with El Campesino (The Farmer). After spending sometime with the Fania All-Stars, Rojas decided to form his own band the "Conjunto Borincano" which was short lived. In 1987 and 1989 he had hits with the salsa versions of the ballards Noche de Bodas (Wedding Night) and Quiereme Como Soy (Love me the way I am). These were accomplished after he joined the "Puerto Rican Power" band.

In 1990, Rojas went "solo" and recorded Condename (1990) and A Mi Estilo (My Style) (1994), however it was his 1995 recording Por Propio Derecho (On my own right), that placed Rojas on the Latin Billboards hit list. He gained the recognition he always wanted when he won a double Platinum Record Award, the Paoli Prize for "Best Salsa Artist of the Year" and an "ACE" Award.

In 1996, Rojas had hits with Humildemente (Humbly) and Pal' Pueblo (For my town), he also released 20th Aniversario, Alegrias y Penas and Navidad con Tito in 1999.