At a campaign rally, he called the South Carolina senator an "idiot" and then told the crowd to try the number.
A Politico reporter called the number on Tuesday, and Mr Graham answered.
Mr Graham recently called Mr Trump "a jackass" and condemned the real estate mogul's comments about Senator John McCain.
Mr Trump has come under increasing criticism from fellow Republicans and veterans groups after he appeared to disparage Mr McCain's war record.
"He's a war hero because he was captured. I like people who weren't captured," he said, referring to Mr McCain's time as a prisoner of war in Vietnam.
Recent national polls show Mr Trump with a double-digit lead over his closest Republican rival.
However the polling was mostly conducted before the controversial comments about Mr McCain.
His rivals are becoming increasingly frustrated as Mr Trump continues to dominate the media coverage of the crowded Republican race.
Mr Trump has drawn headlines since he called undocumented Mexican immigrants "rapists" and "criminals" when he launched his campaign in June.
"The world is literally falling apartâ€¦ and all we're talking about is Donald Trump," Mr Graham told CNN on Monday.
To question the military record of Senator John McCain, a former prisoner of war tortured so brutally that he is unable still to raise his arms above his shoulders, would ordinarily have been suicidal.
But Trump is operating under rules of his own making that are perfectly suited to the voracious metabolism of the modern media, and the hyperventilated style of modern campaigning.
The more outrageous his remarks, the more coverage and social media comment he generates. And the more coverage he receives, the better his polling numbers seemingly become.
Increasingly, notoriety equals popularity amongst a large cohort of Republican voters.
Trump: Master of the demolition derby

Officers from Police Scotland alerted Benbecula Community Council to the scam at a meeting of the council earlier this week.
Sent from Italy, the email involves a fake story about an African man trying to transfer his inheritance to a new account after his father was poisoned.
The use of Gaelic in the email is poor, according to speakers on the isles.
Benbecula Community Council believed the email may have been written using online tool, Google Translate.
Scots Gaelic was added to the service in February this year.

Roy Oliver, 37, fired a rifle into a car that was driving away from a party in the Dallas suburb of Balch Springs in April, killing Jordan Edwards, 15.
His lawyer has not commented. No date has been set for the trial.
The policeman was sacked a few days later for policy violations.
The death occurred when police responded to reports of underage drinking at a house party.
Officers were inside the home trying to find the owner when they heard outside what they believed to be gunshots. Roy Oliver fired into a car full of teenagers as they left the party.
Police had initially said the vehicle reversed "aggressively" towards the officer, but footage discredited the claim, showing the car driving forward, away from him.
He was also charged with four counts of aggravated assault with a deadly weapon by a public official, in relation to the other four teenagers, including two of the victim's brothers, who were in the car.
"It is important to let our community know that justice is proceeding effectively and thoroughly at the Dallas County DA's office," Faith Johnson, the county's district attorney, said in a statement.
The teenager was described by his coach as "a checklist of everything you would want in a player, a son, a teammate, a friend".
Roy Oliver faces five to 99 years in prison on the murder charge, the Dallas Observer reports.
If convicted, he would be the first police officer convicted of murder in Dallas county since 1973, the report adds. He is currently free on bail.
Lee Merritt, a lawyer for the Edwards family, said on Twitter: "We remain cautious. A murder indictment for Roy Oliver is appropriate but the fact is it's been [more than] 40 years since a cop was convicted in [Texas]."
US presidential candidate Donald Trump has given out the mobile phone number of Senator Lindsey Graham - one of his Republican rivals for the White House.
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What is believed to be the first email scam using Gaelic has been targeted at residents of the Western Isles.
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A former police officer who shot an unarmed black teenager in the head has been indicted on a murder charge by a grand jury, prosecutors in the US state of Texas say.