As far as how I would do it is to attach the file to the email, then send the email to an account that you have on the phone. Is this ics file the Gmail calendar? If so, you could add the Gmail calendar to your account if you have Gmail on the iPhone. If you have Gmail on the iPhone, you would just need to turn on Calendar for the account.
How do you import a ics file from gmail into the iPhone calendar ?
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Using gmail to import a ics file