  Recently it was demonstrated that Sr intercalation provides a new route to
induce superconductivity in the topological insulator Bi$_2$Se$_3$. Topological
superconductors are predicted to be unconventional, with mixed even and odd
parity Cooper pairs states. An adequate probe to test for unconventional
superconductivity is the upper critical field, $B_{c2}$. For a standard BCS
layered superconductor $B_{c2}$ shows an anisotropy when the magnetic field is
applied parallel and perpendicular to the layers, but is isotropic when the
field is rotated in the plane of the layers. Here we report measurements of the
upper critical field of superconducting Sr$_x$Bi$_2$Se$_3$ crystals ($T_c =
3.0$~K). Surprisingly, field-angle dependent magnetotransport measurements
reveal a large anisotropy of $B_{c2}$ when the magnet field is rotated in the
basal plane. The large two-fold anisotropy, while six-fold is anticipated,
cannot be explained with the Ginzburg-Landau anisotropic effective mass model
or flux flow induced by the Lorentz force. The rotational symmetry breaking of
$B_{c2}$ indicates unconventional superconductivity with an odd-parity
polarized triplet Cooper pair state ($\Delta_4$-pairing) recently proposed for
rhombohedral topological superconductors, or might have a structural nature,
such as self-organized stripe ordering of Sr atoms.
