There are no definite answers possible for your question, as there is no known number's for anime fans within the programmer community.
Besides that it is still very Dependant on how broad you take the term "programmer" and "like".
There are plenty of children out there that are able to write a simple script and call them self a programmer. And even without those there are tons of programmers that enjoy watching a anime every once in a while, or some times a cartoon. Which roughly would be just as big as the programmer group that likes to watch a movie, television series and even reading a good book.
We can make a well educated guess, but it would be no more then speculation.
Assuming you are aiming at the above average adult anime watching behavior, so where adult are watching just as much as kids. Which is according to the following source roughly 24 hours a week or 3.4 hours a day.
According to TV ratings company Nielsen, kids in 2012, age 2 to 11, watched an average of 24 hours of TV a week. That’s an average of three and a half hours a day.
Taking a average daily life of showering, eating and minimum healthy sleeping habits and jobs into account. A person would take up about at least 19 hours a day, leaving 5 hours a day. With the average programmers age of about 37 years this time is usually spend with wife/ kids. Leaving about 13% tops of programmers above the ago of 20 to even have time enough to above averagely like anime to begin with.