Can I put Valspar gloss finish over an acrylic painting?

I painted my iPhone case white with regular acrylic paint by brush, and I was wondering if I could spray Valspar gloss finish over it?

You may be be able to do this, but I'm not sure it's a very good idea. What are you hoping to accomplish with this?
The purpose of a clear varnish would be (ideally) to reduce fading and scratches - right? I don't know what you consider "regular" acrylics, but if they're a decent quality (not Basics or a store brand student-grade paint) fading won't be an issue. However, acrylics are actually pretty soft. Acrylic artists paint should not be confused with acrylic nails, or hard acrylic plastics - their is actually a pretty wide spectrum of polymers called "acrylic" - and the type used in paint for artists is not really intended for severe wear and tear as might be needed for a phone case.

Here is what you might try… Get a CLEAR acrylic gel, gloss (regular) gel. Brush two coats of that over your acrylic colors. That will even out the sheen so everything is pretty glossy, but it will also provide a fairly thick layer to ward off scratching.

Then, if you like, try some spray varnish. An acrylic spray varnish made for artwork would probably be better, but it is very unlikely that the valspar will hurt the acrylic. To be safe, make sure everything is perfectly dry (not just dry to the touch, give the acrylics at least a day before putting a varnish over them) and ideally do a test piece, not on the phone, to make sure the spray varnish doesn't do anything weird over the acrylics… Like "plasticize" - remain tacky indefinitely, or fog up (most likely if you spray too heavy a coat and/or the acrylic hasn't dried thoroughly), or anything like that.