The short answer is, YES, you can.
That being said, I want to be realistic with you.
Will you make more money with a blog or a website than without one? Yes, absolutely.
Can you make six figures with affiliate marketing without a website or blog? Probably not.
However, I do know dozens and dozens of people that make several hundred to a couple thousand dollars a month with affiliate marketing without having a blog or website.
If you do not currently have a blog or a website I encourage you to start promoting affiliate offers and applying the principles now, so when you DO have a website or blog, you can hit the ground running.