Yes. Here's a sketched example:
Start in L. Let P be the forcing which adds ω1 many Cohen reals, and let G be an L-generic filter for P. Then L(ℝ)L[G] will model ZF, but will have no well ordering of the reals. The point is that if σ is an automorphism of P, then σ can be extended to an elementary map from L[G] to L[σ[G]], and this extension will fix L(ℝ)L[G]. So if there was a well ordering of ℝ in L(ℝ)L[G], it would give a well ordering of G which was fixed by σ. But σ can reorder the elements of G because of the homogeneity of P.