I don't see a problem with subject/verb agreement at all.A cost efficient way to have multiple articles online that contain links back to your site is to utilize one of the many websites that post articles for free."
The subject of the sentence is "A cost efficient way" (singular); the verb is "is" (singular).
If the question is with "one of the many websites that post articles for free" I don't see a problem there either. "one" doesn't have to agree with anything. You're talking about "many websites that post" not "one website that posts."