No (well ... sort of but it is a waste)
All electrical machines need an AC flux to couple the magnetic energy. DC brushed machines produce this via commutators. Basically these are also AC, just expose a DC accepting connection.
So why can't you have a "DC induction machine" Well the defining characteristics of an induction machine are: AC stator & AC rotor & torque generated at any other speed but synchronous.
If you were to feed the machine with DC you would need some form of commutator to take that DC and alternate it to produce the required AC.
Could this AC be enough to excite the rotor with an AC field? ... sure something would be coupled across, but it would not be efficient as the airgap field of a DCmachine is more squarewave.
Imagine a mains transformer being excited with a squarewave, some energy does get transformed but not as much as if it was AC