  We investigate magic-angle twisted bilayer graphene (MATBG) with
proximity-induced Ising and Rashba spin-orbit couplings (SOC) in the top layer,
as recently achieved experimentally. Utilizing the Bistritzer-MacDonald model
with SOCs, we reveal a rich single-particle topological phase diagram featuring
topological flat bands across different twist angles and interlayer hopping
energies. The evolution of Dirac cones and Chern numbers is examined to
understand the topological phase transitions. We find that all phases can be
achieved with an experimentally accessible SOC strength ($\sim$1 meV) in
systems with angles very close to the magic angle. Furthermore, the van Hove
singularity for each topological flat band splits in the presence of SOC,
significantly altering the electronic properties. Additionally, we investigate
the spin textures of each band in momentum space, discovering a skyrmion-like
spin texture in the center of the moir\'e Brillouin zone, which is correlated
with the topological phase transitions and can be tuned via the SOCs and an
out-of-plane electric field. Our findings provide a comprehensive understanding
of the topological flat bands, establishing a foundation for grasping the
intrinsic and rich roles of SOCs in MATBG.
