Rice was born into a Kanien'kehaka (Mohawk) family on the Kahnawake reserve in Quebec, and she is proud of her First Nations heritage. Through her father she is a member of the Rice family of Kahnawake, having descended from Edmund Rice, an early immigrant to Massachusetts Bay Colony. Two Rice boys were taken captive as children in 1704 from Massachusetts, and taken to Kahnawake, Quebec where they were adopted by Mohawk families and became assimilated. Alex is descended from Edmund Rice's great grandson, Silas, who took the name of Tookanowras, but he was also baptized as Catholic and known as Jacques Thanhohorens.

There Rice attended local schools and trained to become a professional Dancer at local dance studios; she developed a passion for acting when she landed a part in an educational video produced at her grammar school. She attended Our Lady of Perpetual Help High School in Brooklyn. In 1990, after her father died and she graduated from high school, Alex and her mother Melody Rice moved back to Kanawake. She attended Dawson College and Concordia University in Montreal, where she earned a degree in library science.

Rice first traveled to California in 1996 to attend a modeling convention and landed her first entertainment job working behind the scenes at the Judge Judy show. Her first feature film was the independent The Doe Boy (2001), which garnered several international film festival awards. She is perhaps best known for her recurring role as Janet Pete in the films Skinwalkers (2002), Dreamkeeper (2003), Coyote Waits (2003), and A Thief of Time (2004), based on the Tony Hillerman novels by the same names. She has appeared in other films including Lewis and Clark: Great Journey West, On The Corner, A Thousand Roads, the IMAX release of Sacagawea, Johnny Tootall and The New World. She has also acted in various television series, including Spin City, CSI, Strong Medicine and The Sopranos.

Rice played Sue Clearwater in the third installment of The Twilight Saga: Eclipse released in 2010, and the fourth and fifth installments The Twilight Saga: Breaking Dawn - Part 1 released in 2011, and The Twilight Saga: Breaking Dawn - Part 2 released in 2012.