Many indexes are available to estimate aridity. Stadler (2005) compiled all of them in the Encyclopedia of World Climatology that you can find here: http://www.springer.com/earth+sciences+and+geography/atmospheric+sciences/book/978-1-4020-3264-6
However, Maliva & Missimer (2012) reviewed some of the most utilized indexes: http://link.springer.com/chapter/10.1007/978-3-642-29104-3_2
These indexes include: AI utilized by the UNESCO (widely used), AIm proposed by De Martonne (1926), and AIt proposed by Thornthwaite (1948).
The Consortium for Spatial Information has data available on global aridity indexes and potential evapotranspiration (required to calculate the AI used by the UNESCO). Here are the links: CGIAR-CSI, and http://www.cgiar-csi.org/data/global-aridity-and-pet-database