The superconducting behavior of the topological semimetal CaSn₃ was investigated by means of magnetotransport and muon spectroscopy (μSR) measurements, both providing strong evidence of nematic behavior. Magnetotransport detects an anisotropic upper critical field, characterized by a twofold symmetry about C₄ axis, thus breaking the rotational symmetry of the underlying cubic lattice. Transverse-field μSR data support such picture, with the muon depolarization rate depending strongly on the magnetic field direction, here applied along the [110] or [001] crystal directions. In the former case, the absence of any additional muon depolarization suggests an unconventional vortex lattice. In the latter case, a vortex lattice encompassing a sample volume of at least 52% indicates the bulk nature of CaSn₃ superconductivity. The resulting superfluid density in the (001) planes shows a gapped low-temperature behavior, with a superconducting gap value Δ(0)≃0.61(7) meV. Additional zero-field μSR results indicate that the superconducting state is time-reversal invariant. This fact and the breaking of rotational symmetry in a fully gapped superconductor are consistent with an unconventional pairing state in a multidimensional representation, thus making CaSn₃ an important example of nematic superconductor.