Accountability in Corporate Political Activity Act of 2010 - Amends the Federal Election Campaign Act of 1971 to prohibit a corporation organized by authority of any law of Congress from engaging in any campaign-related activity if the corporation has been subject to: (1) any federal criminal penalty; (2) a civil money penalty under this Act; or (3) a civil money penalty under any other federal law in an amount equal to or greater than $1 million.