The transverse spin transfer of $\Lambda$ hyperons in proton+proton collisions can provide insights into the polarized fragmentation function and the transversity distribution of the nucleon. In this contribution, we report the first measurement of the transverse spin transfer of $\Lambda$ and $\bar{\Lambda}$ hyperons along the polarization direction of the fragmenting quark in transversely polarized proton+proton collisions at RHIC. The data were taken in 2012 with the STAR detector at $\sqrt{s}=200\,\mathrm{GeV}$ with an integrated luminosity of 18.4 $\mathrm{pb}^{-1}$ and covered hyperon transverse momenta up to 8 GeV/c and $\eta$ range of $-1.2\sim1.2$. The beam polarization was about 63% during our data taking period. The results of the transverse spin transfer, $D_{\mathrm{TT}}$, are consistent with zero within uncertainties. The statistical uncertainty is $\sim0.04$ at the highest $p_{\mathrm{T}}$ bin.