Call here is common jargon in U.S. medicine, and perhaps elsewhere, referring to the duty to be available on short notice outside of regular working hours as part of one's employment. This is the same sense of call as in call schedule and call roster
It is taken from the expression on-call (OALD):
[only before noun] (especially North American English)
(of a doctor, police officer, etc.) available for work if necessary, especially in an emergency
In turn, this derives from call in the sense of a request or demand made of someone.
You can think of call as a type of shift, somewhat analogous to duty or watch in the military, though the nature of it differs somewhat by role, specialty, and experience. For example, for a new doctor in training (known as a resident in the American system), call entails being at the hospital for 28 hours at a time, filling in for other doctors or assisting with surges in demand. At the next level (attending), you do not need to be present at the hospital while on call, but you can never be far from either the hospital or from a telephone as you might be asked to come in on short notice. As you can imagine, call is very unpopular.
The tweet is a play on words. The replier says to Dr. Gu that although he would never take Gu's call duty—that being too undesirable—he will happily take a knee (genuflect) with him.