"staff position" is correct and usable in written English.
You could use it to refer to a job with a company, organization, school, etc. For example: "I applied for a staff position at the university."
He began talking to New York City Ballet, then to A.B.T., about a staff position.
From his staff position he criticized the state of the army's training.
(By this time, Ligsay had been transferred to a staff position at headquarters).
The New Yorker seeks a reporter/researcher for a full-time staff position at newyorker.com.
Three months later, I had a job my first staff position as a writer.
He was named staff director of the House Intelligence Committee, the top staff position, in 1997.
Lewis left the Times after a failure to secure a staff position at the paper.
A city staff position inherently lacks the independence required to serve effectively as a parent advocate.
Later, she worked for the Wilhemina Modeling Agency in a staff position.
After graduating, he moved on to a staff position with the Charleston City Paper in South Carolina.
When some federal money was found to fund a single staff position, he became the project's first employee.
