Robocall Privacy Act of 2010 - Amends the federal criminal code to impose a fine on any individual who knowingly makes or causes to be made a political robocall during a specified period prior to a general, special, run-off, or primary election, to any person between 9 p.m. and 8 a.m. or to the same telephone number more than twice on the same day. Exempts calls in which there is a disclosure at the beginning of the call of the name of the sponsor or originator of the call and that the call is a recorded message. Defines "political robocall" as any outbound telephone call which plays a recorded message that promotes, supports, attacks, or opposes a candidate for federal office and in which a person is not available to speak with the person answering the call.