Rice was born in Shedds, Oregon (later renamed Shedd).
He received a bachelor's degree in electrical engineering from Oregon State University and did graduate work at Caltech and at Columbia University. He worked for nearly forty years at Bell Labs. At Bell Labs, Rice discovered the Rice distribution and Rice's formula. In 1957–58 he was a visiting professor at Harvard University.
His paper “Mathematical Analysis of Random Noise”, published in the Bell System Technical Journal divided over two issues, is considered as a classic reference in its field.