X-ray polarization is a powerful tool to investigate the geometry of accreting material around black holes, allowing independent measurements of the black hole spin and orientation of the innermost parts of the accretion disk. We perform X-ray spectropolarimetric analysis of an X-ray binary system in the Large Magellanic Cloud, LMC X-3, that hosts a stellar-mass black hole, known to be persistently accreting since its discovery. We report the first detection of the X-ray polarization in LMC X-3 with the Imaging X-ray Polarimetry Explorer, and find the average polarization degree (PD) of 3.2% +/- 0.6% and a constant polarization angle of -42(degrees)+/- 6(degrees) over the 2-8 keV range. Using accompanying spectroscopic observations by NICER, NuSTAR, and the Neil Gehrels Swift observatories, we confirm previous measurements of the black hole spin via the X-ray continuum method, a approximate to 0.2. From polarization analysis only, we found consistent results with low black hole spin, with an upper limit of a < 0.7 at a 90% confidence level. A slight increase in the PD with energy, similar to other black hole X-ray binaries in the soft state, is suggested from the data but with a low statistical significance.