Yupp, it sure is!
This is (at least part of) the point of quantum field theories: they are basically what you get when you try to apply the same principles of quantum mechanics - which basically amount to emplacing a limit on information content - to spatially-pervasive fields like the electromagnetic field, as opposed to just particles, and thus allows one to say that the electric (and magnetic!) field near a charged particle, like an electron, is indeterminate just like its position.
The interesting part about this - which is actually a rather nice "boon", is that it turns out when we do this, the quantum-treated "fields" actually turn out to also be able to manifest as "particles", in that fields and particles end up as two sides of the same coin: we can thus even treat the electron as a disturbance in a field, and disturbances in the electromagnetic field, like light, become particles! (Thus, photons!) Mathematically, the two are related by basically "tilting your head" in a mathematical sense(*), what a mathematician calls a "change of basis". I would also go to suggest that this, perhaps, is a rather more faithful-to-theory way to present a "duality" involving particles than the so-called "wave-particle duality": it is a field-particle duality.
(*) At least for the non-interactive case, i.e. considering the fields separately - it's called the "Fock space" construction. We don't have a good maths to describe the interactive case, and instead must resort to hacks: while quantum field theory of a pure field is thus rather elegant, quantum field theory that is useful is actually a giant freakin' hack!