Yes! The manufacturer claims that this product is vegan, making it suitable for Egg free eaters as well.

Is Ground Cayenne (Red) Pepper (1 lb) by Pure Organic Ingredients, Gluten Free, Vegan, Used in Hot Sauces & Spicy Food, Eco-Friendly Packaging Egg Free?

Yes! The manufacturer claims that this product is vegan, making it suitable for Egg free eaters as well.
Egg Free? Ground Cayenne (Red) Pepper (1 lb) by Pure Organic Ingredients, Gluten Free, Vegan, Used in Hot Sauces & Spicy Food, Eco-Friendly Packaging | Spoonful