[2] Adviser has always been the more usual spelling, though advisor has gained frequency in recent years and is a common alternative, especially in North America.
The Associated Press prefers (AP Stylebook) the use of "adviser", but Virginia Tech (style guide) gives preference to "advisor", stating that it "is used more commonly in academe" and that "adviser is acceptable in releases going to organizations that follow AP style".
[6] Purdue University Office of Marketing and Media's Editorial Style Guide gives preference to "advisor".
The US government uses both: Council of Economic Advisers, Office of the Legal Adviser, Deputy National Security Advisor (deputy to the President's NSA), Legal "Advisor" (Office for the Administrative Review of the Detention of Enemy Combatants), that was part of the team tasked to conduct Combatant Status Review Tribunals of captives detained in Guantanamo Bay, and laws Investment Advisers Act of 1940.
[10] The Department of Justice of the United States, Issue 15, printed in 1927 by the Institute For Government Research, uses both spellings: "1.