The user C121 on r/bitcoin explored this topic in the thread Mining Bitcoin by hand.
He states that it takes 3385 integer operations to calculate one double SHA-256 hash.
His conclusion was that you would reach about 0.00003 H/s, or in other terms, it would take about 9.4 hours for one hash, assuming the human in question could do a 32-bit operation in 10 seconds.
He also estimates that you would fill about seventy pages of paper with the calculations per hash.
As Mathias711 pointed out in the comments, Ken Shirriff actually calculated some SHA-256 operations manually and wrote an article about mining bitcoin with pencil and paper. He arrives at an estimate of 0.67 hashes per day, at a vastly uncompetitive energy consumption. ;)