And social media is filled with tributes to Harden's signature look. "I'll take 5% credit," Harden says of the rise of hipster beards around the nation. "I don't want too much. Just 5%."
Does this mean he thinks people in the nations are having beards partially because of him?
Yes, you're exactly right, this means that "he [agrees] that people nation-wide are growing beards partially because of him."
I would say that the key word is "partially" because as Harden has stated, he wants only five percent of the credit.
I would not say that he "thinks" this, again, because he only presumes to assume five percent of the responsibility.
At most, I would say that he "agrees" with the reporter.
The reason I would not use the word, "think," is because, based on the article, it had not been his intention to start a trend nor is it his intention to maintain the beard for trending purposes.
According to the article, he had started it (and continues it) simply for himself because it has become a "part of his persona."
Meanwhile, I would agree with ParaDice's paraphrasing that he "accepts acknowledgement of his contribution."
Your assumption is correct.
"to give credit to somebody for something" = to acknowledge somebody's role in / contribution to an achievement. Best examples: the credits at the end of a movie.
Here you've got the opposite perspective on it: he takes credit, i.e. he (modestly) accepts the acknowledgement of his contribution to the spread of beards.
