The simplest way to do this is to keep a copy of the list used to define the optionmenu. Then you can use the index to get the value from the list and assign it to the associated variable.
For example:
options = ["one","two","three"]
...
self.menuVar = tk.StringVar(master)
self.optionMenu = tk.OptionMenu(master, self.menuVar, *options)
...
self.menuVar.set(options[0])
Another option is to get the menu object associate with the widget, and use menu commands to get the text at the given index, and use that to set the variable:
value = self.optionMenu["menu"].entrycget(0, "label")
self.menuVar.set(value)