  We show that introducing spin-singlet or spin-triplet superconductivity into
twisted bilayer graphene induces higher-order topological superconductivity.
$C_{2z}T$-protected corner states of Majorana Kramers pairs appear at the
boundary between domains with opposite signs of pairing, and zero modes
materialize in Abrikosov vortices. The topology of the superconducting phase
originates from the anomaly [1] -- the absence of a lattice support -- of the
single-valley band structure of twisted bilayer graphene, which is protected by
$C_{2z}T$ and the particle-hole symmetry $\cal P$. We prove that any pairing
(spin-singlet or spin-triplet) term preserving valley-U(1), spin-SU(2),
time-reversal, $C_{2z}T$, and $\cal P$ must drive the system into a
higher-order topological superconductor phase. Here spin-SU(2) is the global
spin-SU(2) for the singlet pairing and a combination of two SU(2)'s in the two
valleys for the triplet pairing. Using a Dirac Hamiltonian, we demonstrate the
existence of corner modes and confirm this with numerical calculations. These
corner states are stable even if the approximate particle-hole symmetry $\cal
P$ is weakly broken, which is true in experimental setups. Finally, we suggest
an experiment to detect the topological superconductivity: by observing the
fractional Josephson effect in a TBG-TSC Josephson system.
