Are there any NFL quarterbacks who retired having an undefeated career as a starter?

No.

Looking at the records for starting quarterbacks, of those who had at least 50 starts, Otto Graham (1921-2003) holds the record with a career winning percentage of 0.814 (57-13-1). [Wins-Losses-Ties]

Tom Brady presently holds the record for the most career wins (245-75-0) for a win percentage of 0.766 although those numbers are subject to change, since he is still playing.

Brady's record is a long way in front of #2 Brett Favre's 0.624 (186-112-0).

It would theoretically be possible for a quarterback to retire undefeated... say someone who won a handful of games before a career-ending injury. However, statisticians do not like to stack such outliers up against those with lengthy careers and generally insist on a certain number of starts before making comparisons.

Reference: https://wiki2.org/en/List_of_National_Football_League_career_quarterback_wins_leaders+Milds.2

I spent some time searching through records at the Football Database (footballdb.com). They have won-loss records for all QBs since the 1970 season.

There are a handful of quarterbacks that have 1-0 or 2-0 records as a starter. I won't list them all. One, Ed Rubbert of the Washington Redskins, had a 3-0 record as a starting QB. He was a replacement player in the 1987 NFL season, the year that there was a players' strike. He won all three games he started. According to Wikipedia, Rubbert inspired Keanu Reeves's character in the movie "The Replacements".

I should note that Cooper Rush, the current QB for the Dallas Cowboys, is 4-0 in his four starts (as of now). However, he is not retired and therefore does not fit your criteria.

https://www.footballdb.com/players/ed-rubbert-rubbeed01
https://en.wikipedia.org/wiki/Ed_Rubbert