My Autocorrect is telling me to change it to "biceps curl". Also, the Wikipedia entry is Biceps curl.
Is "bicep curl" wrong and if so, why?
It is "wrong" in the sense that "biceps" is not a plural word to begin with. The word was directly borrowed from Latin where singular nouns can end in 's'.
The ceps in biceps, triceps, and quadriceps comes from the Latin word for “head”; the literal meaning of biceps is “two-headed,” referring to a muscle that has two attachments to the bone (this definition of head is “the end of a muscle nearest its origin”).
However, the usage of "bicep" is common enough that in common writing almost all readers would understand what you mean.
In fact, bicep is used frequently enough that it is entered in the dictionary, where it is defined as a synonym of biceps. Its first recorded use is 1939.
("Usage Notes: Is the Word 'Biceps' Plural or Singular?", Merriam-Webster)