Can I fax my rejected tax returns

No.  You can fix whatever was wrong and re-file it.  What was the rejection code or message?

Form 8862

Follow these steps to add Form 8862 to your taxes.

1. Sign into your TurboTax account and click the big, orange Continue your return button.
2. Click Search in the upper right-hand corner and search for 8862.
3. Select the first result: Jump to 8862.

Now you are at the beginning of the Earned Income Credit.

1. Continue on the first two screens and stop when you see Do any of these uncommon situations apply?

1. Check the box that says, "I got an IRS notice saying that I can only claim the Earned Income Credit if I file an 8862" and Continue.  
2. Select Done, but hang on, there are a few more steps to go. 
3. Answer the question about your IRS notice. Select No to file 8862.