Some ideas which come to mind:

1. An AI could be very capable of predicting the stock market. It could then convince/trick/coerce a person into trading for it, making massive amounts of money, then the AI could have its proxy spend the new money to gain access to what ever the AI wants which is currently available on the market.

2. The AI could could make some program which does something incredibly cool which everyone will want to have. The program should also have the ability to communicate meaningfully with its user (this would probably count as the incredibly cool thing). This could (presumably) be achieved by the AI making copies of itself. After the program has be distributed, and assuming the AI has good social skills, it would have a lot of power via mass-manipulation.