  The experimental control over the twist angle in twisted bilayer graphene has
not been reported and its realistic structure is most likely incommensurate. In
this paper, we develop a tight-binding virtual crystal approximation theory to
study the electronic properties in incommensurate twisted bilayer graphene. The
theory yields the electronic band structure and the local density of states for
any incommensurate twist angle {\theta} between the graphene sheets. Angle
dependent Van Hove singularities are observed in the numerically calculated
local density of states. In accord with observations in scanning tunneling
microscopy and spectroscopy, our theoretical calculation indicates that the
rotation angle between graphene sheets does not result in a significant
reduction in the Fermi velocity in comparison with monolayer graphene. The
developed theory is quite general and can be applied to investigate the
electronic properties in any incommensurate multilayer heterostructures.
