  Broken symmetries play a fundamental role in superconductivity and influence
many of its properties in a profound way. Understanding these symmetry breaking
states is essential to elucidate the various exotic quantum behaviors in
non-trivial superconductors. Here, we report an experimental observation of
spontaneous rotational symmetry breaking of superconductivity at the
heterointerface of amorphous (a)-YAlO$_3$/KTaO$_3$(111) with a superconducting
transition temperature of 1.86 K. Both the magnetoresistance and
superconducting critical field in an in-plane field manifest striking twofold
symmetric oscillations deep inside the superconducting state, whereas the
anisotropy vanishes in the normal state, demonstrating that it is an intrinsic
property of the superconducting phase. We attribute this behavior to the
mixed-parity superconducting state, which is an admixture of \emph{s}-wave and
\emph{p}-wave pairing components induced by strong spin-orbit coupling inherent
to inversion symmetry breaking at the heterointerface of a-YAlO$_3$/KTaO$_3$.
Our work suggests an unconventional nature of the underlying pairing
interaction in the KTaO$_3$ heterointerface superconductors, and brings a new
broad of perspective on understanding non-trivial superconducting properties at
the artificial heterointerfaces.
