Graham plans to investigate Ukraine operation at Senate Intelligence Committee after Trump's impeachment trial is over.
The post had been removed by Saturday morning, but unmasking the whistleblower could violate federal protection laws.
"Why is Twitter failing ... to suspend accounts of people who are trying to get the whistleblower killed by naming the person?" asks former U.S. ethics chief.
Her father has repeatedly urged the public outing of the person who raised concerns about his call with Ukraine's president.
The newspaper explained how the president's targeting of the official who sparked the impeachment inquiry poses "a grave threat."
The letter, signed by 90 former officials, stressed the importance of protecting the whistleblower's identity, The Wall Street Journal reported.
Democrats say a federal employee has "evidence of possible misconduct" concerning the president's taxes.
In a letter forwarded to lawmakers, lawyers for the anonymous whistleblower wrote they have "serious concerns."
The president said he wants to meet the whistleblower behind the complaint fueling his impeachment inquiry, despite threatening the person last week.
The president's allies fanned out across the Sunday talk shows with myriad responses.