It depends. You can refinance a private student loan with a variable interest rate to a private student loan to a fixed interest rate. You can also refinance a federal student loan to a private one, but this could prove to be a refinancing mistake to avoid, since you’d lose the hardship benefits that come with federal student loans.
What you can’t do is refinance a private student loan with a variable rate to a federal student loan. In fact, you can never refinance a private student loan to a federal, no matter what type of interest plan you have.