The phrase "assign her to" is correct and usable in written English.
You can use it when you want to designate a specific task or responsibility to someone, usually in a professional or official context. For example, "The team leader assigned her to lead the project."
He said he would assign her to oversee the county's Office of Cultural Affairs.
Might as well assign her to some work that would interest her, he said.
At a church gathering, Bishop H.H. Brookins called her aside and told her he wanted to assign her to Payne.
The success emboldened Mr. Miller to assign her to other novelty songs, most notably "Botcha Me" and "Mambo Italiano" that also became hits.
"So radically do her novels differ from one another (the spareness of 'Standard Dreaming,' for instance, set beside the baroque complexities of 'The New Yorkers'), it has been impossible to assign her to the sort of ready-made category that literary journalism seems too often to insist upon".
They had discussed firing her, but this could have led to endless litigation, which the Times might lose; they could "negotiate a severance deal"; or they could "put her in a job where she would be genuinely contained" — for instance, assign her to the News Service division, part of the business department, and on another floor.
From there, Chen Sam's firm hired her, and assigned her to assist in working for Ms. Taylor.
She told her sister no, and assigned her to hold her bouquet and fluff her long ivory train.
She wrote scripts, too, and in 1927 Paramount Pictures assigned her to direct "Fashions for Women".
In time, Lackman assigned her to a cafeteria in a high-rise, and she went back to work.
Instead, federal prison officials assigned her to a high-rise detention center, where nearly 1,000 inmates inhabit 11 floors.
