There is no option to associate a variable with a text widget. You can achieve the same thing by using variable traces and widget bindings but it's rarely worth the effort.
The typical way to interact with the text widget is to read a file into a variable then use the insert
method of the widget to put the text into the widget. Then, to save you just do the reverse -- get the text from the widget with the get
method, and write the data to a file.
One tip: when you do a get, don't get the text from 1.0 to "end", use "end-1c" instead. If you specify "end" as the last character you'll get the implicit newline that tk always adds, meaning your text file will grow by one character each time you do a load/save cycle.