We calculate the electroweak-like one-loop supersymmetric contributions to the rare and flavor-violating decay of the top quark into a charm quark and a gauge boson: t>cVt->c V, with V=γ,Z,gV=\gamma,Z,g. We consider loops of both charginos and down-like squarks (where we identify and correct an error in the literature) and neutralinos and up-like squarks (which have not been calculated before). We also account for left-right and generational squark mixing. Our numerical results indicate that supersymmetric contributions to t>cVt->cV can be upto 5 orders of magnitude larger than their Standard Model counterparts. However, they still fall short of the sensitivity expected at the next-generation top-quark factories.Comment: 13 pages, LaTex, 1 figure included. Final version to appear in Physical Review D. Chargino contribution dealt with in greater detail. Minor revisions in tex

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