Wordorigins.org

The original sense of dork is penis. It is probably an alteration of dick, dating to the early 1960s.

From Jere Peacock’s 1961 Valhalla, in a reference to 1953:

You satisfy many women with that dorque?

In 1964, the term was captured in the May 1964 issue of American Speech:

The word dick itself serves as a model for two variants which are probably Midwestern, dirk and dork, also meaning “penis.”

The sense of a contemptible person dates to at least 1967. From Moser’s and Cohen’s Pied Piper of that year:

I didn’t have any clothes and I had short hair and looked like a dork. Girls wouldn’t go out with me.

Some contend, incorrectly, that dork originally meant a whale’s penis. That’s only half right; there is nothing particularly cetacean about the word.

(Source: Historical Dictionary of American Slang)