"Being a U.S. Senator representing Texas, it makes sense he should be only an American citizen," Frazier said in an email.
Cruz, 43, was born in Calgary, Alberta, in 1970, while his parents were working in the oil business there. His mother, Eleanor, is from Delaware, while his father, Rafael, is a Cuban who didn't become a U.S. citizen until 2005.
Though he has been in office only about 18 months, Cruz helped lead last year's partial government shutdown and has become a conservative grass-roots champion across Texas and the country.
Amid questions last August about his eligibility to be president should he decide to run, Cruz released his birth certificate to the Dallas Morning News — and said then that he was surprised to learn he was a dual Canadian-U.S. citizen.
Upon learning that he'd received it at birth, he promised to formally give it up. Months then passed before Cruzhired an immigration attorney to help him with the process.
Frazier provided a copy of Cruz's Certificate of Renunciation, which certifies that Rafael Edward Cruz "has formally renounced Canadian citizenship and pursuant to the Citizenship Act will cease to be a citizen."
Still, the citizenship issue could still be a thorny one for Cruz. Some conservatives claimed President Barack Obama was born in Kenya and thus not eligible to be U.S. president. Obama is an American citizen; his father was Kenyan, his mother American.
The U.S. Constitution says only a "natural born Citizen" may be president. Legal scholars, however, generally agree the description covers foreign-born children of U.S. parents.
Previous foreign-born Americans — notably Republicans John McCain and George Romney — have run for president with some mention, but no serious challenges, of their eligibility.
Cruz, who has made frequent trips to Iowa, New Hampshire and South Carolina, the first three states to hold presidential contests, has refused to say if he plans to run for president.
Asked about his presidential eligibility at the Texas Republican Convention last week, Cruz said, "I've disclosed all the relevant facts. As you know, I was born in Canada. My mother was a U.S. citizen at the time of my birth. She was a U.S. citizen from birth so, under U.S. law, I'm an American citizen by birth."
"Beyond that," he added, "I will leave the legal consequences of those facts to others to worry about."