Putin has repeatedly identified himself with Unified Russia without being a card carrying member, but he is not widely seen as representing the party.
1995; Unity, and Fatherland/All Russia in 1999; Unified Russia in 2003. In all cases, to various degrees, each mutation presented itself to voters as the "party of power" and espoused more or less the same political rhetoric -- a mixture of liberal, conservative, national, and social messages.