Based on the reading of "Anansi Stories" in "Tiger's Sheep-Skin Suit", Anansi framed Tiger because Anansi wants to get two hundred pounds and the best daughter to marry from Mr. Mighty. This resulted in Tiger sent to prison for ten years. Hope this answers your question.
He wants to get the reward for finding the thief (daughter and money). But because he’s the thief, he has to blame someone else, and Tiger isn’t very smart.
