After a two-year junior career in the United States Hockey League (USHL), Alberts was selected by the Boston Bruins 179th overall in the 2001 NHL Entry Draft. Following the draft, he joined the college ranks with Boston College of the Hockey East conference. In four seasons with the Eagles, Alberts was named Hockey East's Best Defensive Defenseman and was a two-time NCAA All-American. Joining the Bruins in 2005, he played three seasons with the club before being traded to the Flyers. He played with the Flyers for one year, then with the Hurricanes in 2009. At the trade deadline the following year, he was traded to the Canucks. Internationally, Alberts has competed for the United States at the 2006 and 2007 World Championships.