WASHINGTON—A senior Republican senator on Tuesday called for sanctions against Saudi Arabia over the disappearance and presumed killing of a dissident journalist in the kingdom’s Istanbul consulate this month, and said he would not return to the kingdom as long as Crown Prince Mohammed bin Salman remains in power.

In an interview on Fox News, Sen. Lindsey Graham (R., S.C.) said it was up to President Trump to decide the U.S.’s course of action, but he said, “I know what I’m going to do: We’ll sanction the hell out of Saudi...