Affiliate links will affect your search engine rankings either your an affiliate marketer or the merchant.

I agree with the secomd answer that as a merchant you benefit a lot from your affiliate program and get a lot of backlinks of your affiliates promote the their links.

But as an affiliate if you to increase your search engine ranking for a particular affiliate link, then you will need to either write review for the product you promote and use the product name in an archor text.

The only way it will affect your search engine ranking is when you use the product in your review or article more than once.