Born in Santiago, Brazil, da Rosa began his career at the youth ranks of his hometown club Caxias.
In 1999 Álex arrived in Bolivia for the first time and signed for big club Oriente Petrolero, however, he did not live up the expectations and left after a couple of months.
For the next three years, he maintained a good form and scored several goals for the club, helping The Strongest win two national titles in that period.
In 2005, he relocated to Germany to join Bonner SC, before transferring to Colombian team Deportes Tolima the following year.
He scored his first international goal for Bolivia on April 1, 2009, in a memorable victory over Argentina by 6–1 in La Paz.