A better alternative may be to frame it differently

    If applicable, please enter your gift card number.

This implies it is single use though.

Another option is to provide the field when user is already very invested. For instance, he has entered shipping details, contact details etc.

I wonder if anyone has split tested "enter coupon" phrases which doesn't encourage shopping cart abandonment?

The other option is to offer them notification whenever new coupons are available. It is a good way get people who might have abandoned the shopping cart anyway to opt in.