Can I connect my Vietnamese mastercard debit card to my American apple account?

Unfortunately Apple used to at least say something in its documentation but now doesn't say anything either one way or the other.

Payment methods that you can use with your Apple ID - Apple Support used to say this but no longer does: "Make sure that the billing address for your payment method matches the billing address for your Apple ID. In some cases, you might need to call your bank or financial institution to authorize international or online purchases. You might also need to confirm that the mobile number associated with your payment method is correct."

You can try contacting Apple but since their documentation is unclear I don't know if you can get a reliable answer from somebody reading the same documents we do.

To contact Apple, click here --> Choose your country or region - Official Apple Support

Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.

or:

Contact Apple for support and service by telephone --> Contact Apple for support and service - Apple Support

No, I do not believe so. You will need a U.S. credit card or you will need to purchase iTunes gift cards in the U.S.