"Merci" (مرسی)
This translates directly to "thank you" and is the most common and polite way to respond to birthday wishes in Farsi.
You can also add a more personal touch with:
* "Tavalodet shoma ham mobarak" (تولد شما هم مبارک) - "Happy birthday to you too"
* "Be sehat va salamat" (به سلامت و صحت) - "To health and well-being"
* "Omre daemi" (عمر دایمی) - "May you have a long life"
Remember, saying "merci" is always appropriate and shows gratitude for the well wishes.