Incorrect spelling, explanation: this spelling is a mistake because it lacks one additional -m. When creating a new word in English, we must remember to add an additional consonant if there’s a single vowel before the last (and stressed as well) consonant. That’s why the form programer is incorrect. The only correct one is programmer.

Correct spelling, explanation: the noun programmer is a derivative of another noun: program. When looking at similar words, you can observe an important rule: double the final consonant if the word ends in one vowel and one (and stressed as well) consonant. If you do that, you’ll get the correct form: programmer. The suffix -er means someone or something performing a particular action. Don’t spell this word as programer.

Definition of programmer:
noun, a person who programs computers
You can earn good money as a programmer, so why don’t you look for a job like that?
Mike was recently employed as a programmer.