Does the rise of acceptance in "/" for "or" come from the use of "|" in computer programming (For "OR")?
If not is there any correlation?
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The concept of computer programming includes at least formal logic, circuit design, and the use of modern programming languages. For simplicity, I'll just take Babbage's difference engine of 1822 as a convenient starting date for the sake of comparison.
In English, the virgule dates back to the mid 19th century according to Oxford Dictionaries, so may be argued to start around the same time as computer programming. However, it traces its etymology to usage "as a comma medieval MSS" (etymonline). Arguably, the concept of disjunction was already inherent in this usage.
Note that "/" isn't always simply a logical or in English. An example from thepunctuationguide is office/dining room, in which "/" is equivalent to the Latin preposition cum, as in *office-cum-dining room", where it has an element of conjunction. Compare the Latin phrase summa cum laude - it isn't simply best or praised - it's both (excuse my poor Latin).
The vertical bar as disjunction in computer programming can be traced back to the Backus-Naur Form (follow the links in this stackoverflow answer) from about 1958 or 1959 (see also ALGOL 58), where the vertical bar represents choice. Here's an example of such an expression:
digit ::= "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"
So there seems to be little correlation between the etymology of the disjunctive "/" in English and that of computer programming's "|", other than perhaps that both are particularly visual representations of some kind of list separator.