On account of es un sinónimo de because of y en general se debe traducir con por.

Ejemplo
On account of his drinking he was not allowed to teach anymore.
Por su adicción al alcohol no le era permitido seguir enseñando.
They were having a party on account of their winning the match.
Por haber ganado el partido hicieron una fiesta.
Many people were having a walk on account of the nice weather.
Por el buen tiempo mucha gente salió a pasear.