"position as director" is correct and can be used in written English.
For example, "John has worked hard to get to the position as director."
In October 2008 Zerhouni stepped down from his position as director of the NIH.
Mr. Petraeus stepped down in 2012 from his position as director of the Central Intelligence Agency.
Still, something prompted David Petraeus's resignation from his position as director of the C.I.A., right?
Last year, Morgan stepped down from the position as director and now serves as deputy director.
Ira Silverberg is stepping down from his position as director of literature programs at the National Endowment for the Arts.
Miller has stepped down from his position as director of MIT's Space Systems Laboratory SSLL) to accept the NASA appointment.
Mr. Cook is annoyed that Mr. Craig will not respect his position as director of Campo border operations for the Minuteman Project.
It is thought that a new post of head of entrepreneurship within the unit will outrank Ms Usher's position as director of screen.
He left his public-school teaching job over the summer and started a position as director of maker spaces at a nearby private school.
It accelerated rapidly when in 1961 she found a secure position as director of Univers, the largest Romanian publishing house for foreign literature in translation.
In 1953 he was elected to the Diet (parliament) and in 1962 secured his first cabinet position, as director general of the Economic Planning Agency.
