  We employ general arguments and numerical simulations to show that unpaired
Majorana zero modes can occur in cores of Abrikosov vortices at the interface
between a three-dimensional topological insulator, such as Bi$_2$Se$_3$, and a
twisted bilayer of high-$T_c$ cuprate superconductor, such as
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. When the twist angle is close to $45^{\rm
o}$ the latter forms a fully gapped topological superconductor up to
temperatures approaching its native $T_c\simeq 90$K. Majorana zero modes in
these structures will persist up to unprecedented high temperatures and,
depending on the quality of the interface, may be protected by gaps with larger
magnitudes than other candidate systems.
