Mora once attended Colegio de las Hermanas Betlemitas and first played in Cóndor Futbol Club of San Miguel as goalkeeper at an early age. He also played for the San Miguel's city team in the Provincial Games and was picked as goalkeeper for the province team to play the national teen/amateur championship in Ecuador. Mora was then discovered and invited to train in Centro Deportivo Olmedo, while playing as goalkeeper in a friendly match against his college Escuela Politécnica de Riobamba.
Mora has made 20 appearances for the Ecuadorian national team, and made his first full-fledged senior appearance against Italy, a friendly match played in New Jersey. The game ended in a 1–1 draw and to Mora's credit, his penalty save from superstar Luca Toni forced many to take notice, including Luis Fernando Suarez, Ecuador's former Colombian coach.
He played first choice goalkeeper for the Ecuador national team during 2005's 2006 FIFA World Cup qualification. In the 2006 World Cup, Mora played all four matches before his team was eliminated in the Round of 16 by England. Mora allowed 4 goals but kept clean sheets against Poland and Costa Rica. However, due to poor friendly results and a bad Copa America 2007 he has failed to break with the national team.