It doesn’t look like you can unless you are an employee of APS:
https://go.boarddocs.com/vsba/arlington/Board.nsf/files/BR3P6E62DF95/$file/J-5.3.30%20Admissions.pdf
If you were a resident in Fairfax and moved to another jurisdiction, FCPS does offer the option to pay tuition.
Just move your child. They’ll be fine. It’s important for her to build relationships with kids where she lives and attends school.