Historically, straws have been made from paper but today polypropylene plastic is the material of choice. Polypropylene is a resin made by polymerizing, or stringing together, molecules of a propylene gas. When a very large number of these molecules are chemically hooked together they form this solid plastic material.
Today's straws are made of polypropylene, a resin of plastic known by the number 5 in the resin identification code. Polypropylene itself is a highly recyclable plastic resin, commonly used in yogurt containers, bottle caps, toothbrushes and plastic utensils.
To summarize, plastics in categories #2, #4 and #5 are generally considered safe.