Cover your bowl with plastic wrap, making sure to have the plastic wrap touching the surface of the ice cream base so it does not get a skin. Refrigerate for at least 3 hours.
While your ice cream is churning, make your cream cheese swirl by whisking together all of your ingredients until smooth and combined. Place in your fridge until ready to use.
Spoon half of the red velvet ice cream into your loaf pan. Place half of your cream cheese mixture on top and swirl with a knife. Repeat with remaining red velvet ice cream and cream cheese mixture. Freeze for at least 4 hours, or until solid.