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If you cannot control/set the CORS origin policy in the server then there is nothing much you can do from a VUEJS app from the browser. Its the browser which restricts this. You can also ask them if they have jsonp support. Here is a link how to do that.
If everything fails, then write up a small backend service which retrieves the Access Token from the API and can pass the token to the VUEJS app in the browser.
Source:stackexchange.com