The transition magnetic moment for Majorana neutrinos is studied in a simple extension of the Standard Model. This extension incorporates two scalar Leptoquarks $S_1$ and $\widetilde{R}2$ with quantum numbers $(\bar{3},1,1/3)$ and $(3,2,1/6)$ respectively. It is found that these Leptoquarks generate a sizable transition magnetic moment, particularly when the quark bottom is running in the loop. For our analysis of the parameter space, we include the latest measurement of the muon magnetic moment and combine it with the experimental constraint on the branching ratio Br$(\tau \to \mu \gamma)$. We found that, despite the recent agreement on the $(g-2)\mu$ value, large values for Leptoquark Yukawa couplings are allowed due to a degeneracy in the parameters.