According to the VA state tax agency website, Virginia takes up to four weeks to process e-filed tax returns and 8 weeks for paper filed.
But there could be some delays as states crack down on the large number of fraudulent returns.
First, if you efiled the VA return, check with this tool to be sure your state return was successfully efiled and accepted:
https://shop.turbotax.intuit.com/efile/efile_status_lookup.jsp
Here's
how to track the Virginia state refund. After you click on Virginia,
the new FAQ will have a link on how to check on the refund, and also a
link on how to contact the VA state tax agency.
FAQ: How do I track my state refund?
https://ttlc.intuit.com/replies/3300211