My assumption has always been that the programming term originated from the following definition of the word “string” (from Merriam-Webster):
(1): a series of things arranged in or as if in a line <a string of cars> <a string of names>
(2): a sequence of like items (as bits, characters, or words)
Since a string in programming is simply an ordered sequence of characters, referring to this as a “string of characters” (or simply “string”) seems like the most probable origin.