Yes, you can, but it may take a little extra work. First, as the trustee of your trust, you have the same ability to manage your property and finances as you did before you put your assets into your trust. When you refinance your house, the lender will qualify you just like everybody else.
Most title companies take your house out of your trust when you refinance
The “catch” is this: most title companies will take the house out of the trust when they refinance. This means that after your refinance is complete, you will have to create a trust transfer deed, and record it yourself. Some title companies will help you with this, so be sure to ask!
So be sure to put it back when the refinance is complete
Bottom line: of course you can refinance, just be sure your property is in the trust when the refinance is complete.