"Self-Learner" reads like a kenning or nonce phrase.
"Autodidact" appears to enjoy greater popularity:
Edit: If you do not understand how this phrase could seem problematic to a native English speaker, please consider the following phrases: (and their popularity)
The second example occurs most often as a colloquialism, particularly where the speaker is assumed to lack formal education or familiarity with English language mechanics.
Here is an example from the first chapter of Huckleberry Finn:
After supper she got out her book and learned me about Moses and the Bulrushers [...]