No, all presidents must be citizens of the United States by virtue of the US Constitution.
Being the child of US citizens is the only way that an individual who was born outside of the country may be qualified to be president.
No one born outside of the United States has ever won the presidency. The closest thing we have ever had to a president who is a "immigrant" is:
Three years prior to Arizona's statehood, presidential contender Barry Goldwater was born in the Territory of Arizona. In 1964, he was the Republican nominee, but Lyndon B. Johnson won.
John McCain, a contender for president, was born to US citizens in the Panama Canal Zone. Barack Obama emerged victorious in his 2008 race as the Republican nominee.
Other notable people are:
George W. Romney, a presidential candidate, was born in Mexico to US citizens for parents. Despite running for president, he was not selected as his party's nominee.
Lowell P. Weicker, a presidential contender, was born in France to American citizens. Despite running for president, he was not selected as his party's nominee.
Ted Cruz, a presidential candidate, was born in Canada to a US citizen mother. Despite running for president, he was not selected as his party's nominee.
Tulsi Gabbard, a presidential candidate, was born to US citizens in American Samoa. Despite her party not nominating her, she did not win the presidency.
Despite being a US territory, American Samoa does not automatically grant its citizens US citizenship at birth.
Being the child of US citizens is the only way that an individual who was born outside of the country may be qualified to be president.
No one born outside of the United States has ever won the presidency. The closest thing we have ever had to a president who is a "immigrant" is:
Three years prior to Arizona's statehood, presidential contender Barry Goldwater was born in the Territory of Arizona. In 1964, he was the Republican nominee, but Lyndon B. Johnson won.
John McCain, a contender for president, was born to US citizens in the Panama Canal Zone. Barack Obama emerged victorious in his 2008 race as the Republican nominee.
Other notable people are:
George W. Romney, a presidential candidate, was born in Mexico to US citizens for parents. Despite running for president, he was not selected as his party's nominee.
Lowell P. Weicker, a presidential contender, was born in France to American citizens. Despite running for president, he was not selected as his party's nominee.
Ted Cruz, a presidential candidate, was born in Canada to a US citizen mother. Despite running for president, he was not selected as his party's nominee.
Tulsi Gabbard, a presidential candidate, was born to US citizens in American Samoa. Despite her party not nominating her, she did not win the presidency.
Despite being a US territory, American Samoa does not automatically grant its citizens US citizenship at birth.