The most common and most likely answer to this crossword clue is the 6 letter word INVOKE
I've seen this crossword clue in The Guardian
I
N
V
O
K
E
More clues leading to the result INVOKE
Buddy explains!

The straight part
We know that "Call on" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case call on = invoke.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does INVOKE mean?
INVOKE verb- To call upon (a person, a god) for help, assistance or guidance.
- To solicit, petition for, appeal to a favorable attitude.
- To call to mind (something) for some purpose.
- To appeal for validation to a (notably cited) authority.
- To conjure up with incantations.
- To bring about as an inevitable consequence.
- To cause (a program or subroutine) to execute.