The rare flavor-changing top quark decay t → cZ is a clear sign of new physics and experimentally very interesting due to the huge number of top quarks produced at the LHC. However, there are few (viable) models which can generate a sizable branching ratio for t → cZ - in fact vectorlike quarks seem to be the only realistic option. In this paper, we investigate all three representations (under the Standard Model gauge group) of vectorlike quarks (U, Q₁ and Q₇) that can generate a sizable branching ratio for t → cZ without violating bounds from B physics. Importantly, these are exactly the three vectorlike quarks which can lead to a sizable positive shift in the prediction for W mass, via the couplings to the top quark also needed for a sizable Br(t → cZ). Calculating and using the one-loop matching of vectorlike quarks on the Standard Model effective field theory, we find that Br(t → cZ) can be of the order of 10^-6, 10−5 and 10^-4 for U, Q₁ and Q₇, respectively, and that in all three cases the large W mass measurement can be accommodated.