Can I claim for the Recovery Rebate Credit if my filing status changed within 2020? Received both stimulus payments based on my 2019 taxes under "Single" but got married.

The filing status should not matter.  You say you received both stimulus payments, did your spouse receive both stimulus payments?  When you complete your return you will be asked the amount you and your spouse received in stimulus payments.  If you did not receive the full amount for both spouses, it will be made up with the Recovery Rebate Credit.

 

If you did not receive your first and/or second stimulus payment or if the amount received is not correct, you can claim it on your 2020 tax return as the Recovery Rebate Credit.

 

In TurboTax Online, to claim the Recovery Rebate credit please do the following:

1. Sign into your account and continue from where you left off
2. Click on Federal in the left-hand column, then on Federal Review on the top of the screen
3. On the next page titled Let's make sure you got the right stimulus amount, click on Continue
4. Follow the interview
5. TurboTax will determine whether you are entitled to any additional stimulus
6. Any stimulus amount remaining due to you will show as a credit on line 30 of your form 1040.

My spouse is not eligible to receive any stimulus payments since she is a foreign spouse, and I am filing from outside of the States. 

As @CatinaT1 mentions your filing status is not a factor.  Since you are the only one eligible on your joint return and you have received the stimulus payments in rounds one and two, your Recovery Rebate Credit will be reduced to zero on your tax return.  

 

TurboTax will do the calculations based on your entries.  Your return will show you are eligible for 1200 and 600 (total 1800) and that you already received (1200 and 600).  

 

Here is a link with more information.