Depending on what you mean by "geometric", maybe - there's been attempts at constructing theories where the electromagnetic field is also, like gravity, a produ

Depending on what you mean by "geometric", maybe - there's been attempts at constructing theories where the electromagnetic field is also, like gravity, a product of spacetime geometry; these generally involve adding extra dimensions to give spacetime enough freedom to hold those behaviors, and then curling up the extra dimensions small enough to explain why we hadn't noticed them yet. (String theory is one of the distant descendants of these attempts.)