There are rules about how to do it but generally yes you can use a device type AFCI in the first outlet on a branch circuit if it is less than 50' away (wire length). The easiest way to comply is to use a piece of MC cable between the box and the panel. If it is a straight shot you could even use a piece of EMT or a close nipple for a side by side install. It just has to be in metal.
Before I did all of that I would try it on a GFCI only circuit. If that trips look inward toward the fridge. It is not uncommon for old fridges with bad compressors to trip GFCIs.
