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We analyze the orbital magnetic susceptibility from the band structure oftwisted bilayer graphene. Close to charge neutrality, the out-of-planesusceptibility inherits the strong diamagnetic response from graphene.Increasing the doping, a crossover from diamagnetism to paramagnetism isobtained and a logarithmic divergence develops at the van Hove singularity ofthe Moir\'e lattice in the first band. The enhanced paramagnetism at the vanHove singularity is stronger for relatively large angle but gets suppressed bythe flat spectrum towards the vicinity of the first magic angle. A divergingparamagnetic susceptibility indicates an instability towards orbitalferromagnetism with an orbital out-of-plane magnetization and a Landau levelstructure. The region of instability is however found to be practically verysmall, parametrically suppressed by the ratio of the electron velocity to thespeed of light. We also discuss the in-plane orbital susceptibility at chargeneutrality where we find a paramagnetic response and a logarithmic divergenceat the magic angle. The paramagnetic response is associated with negativecounterflow current in the two layers and does not admit a semiclassicaldescription.

Moir\'e lattice effects on the orbital magnetic response of twisted bilayer graphene and Condon instability