Sorokin, the chief executive of the organising committee for next year's tournament, was elected by acclamation at an extraordinary UEFA Congress on Wednesday. He was the only candidate.
Russia had been without a representative on the global governing body's FIFA Council since May when Deputy Prime Minister Vitaly Mutko was barred from standing for re-election.
FIFA said that Mutko had failed an eligibility test by its review committee because his ministerial role contravened the organisation's statutes over political neutrality.
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Mutko dismissed the decision at the time, saying FIFA had changed its criteria.
(Writing by Brian Homewood; Editing by John O'Brien)
