Acceptance is the act of accepting or receiving.
Acceptation is another word for acceptance, especially with the connotation of the object being well-received, or being approved of by the recipient. Acceptation also has a linguistic meaning of the generally understood definition of a word. This word is rarely used (outside of the French language) and even more rare to find it in its linguistic definition. Your safe bet is to stick with acceptance.
Side note: Sometimes acceptation is confused with exception, which describes something as being left out of the group or does not adhere to a general rule.
Lastly, acception was a valid word in the past, but it has now become obsolete.
According to a report, Rowling also sent a wand, an autographed Harry Potter book, Hogwarts acceptance letter, and school supply list. [Fox Chicago]
The Shiite clerical leadership in Najaf represented by the reverend Ayatollah Ali al Sistani has stressed that the new Iraqi prime minister should have a nationwide acceptance among Iraqi sects and nationalities. [Telegraph]
The concept must reach popular acceptance, but could be “absorbed into the commercial world in the next decade or two,” he says. [CNN]
The book “containing the records of our dead which shall be worthy of all acceptation” has now been identified. [Deseret News]
As well, public affirmation of the Bill through the preponderating disposition of parliamentary acceptation is all that is required to give moral freedom to “truth” to operate as it should in the public space. [Ghana Web]