SAN FRANCISCO — In a ballroom at the Olympic Club, a grand, early-20th-century building at the foot of Nob Hill, Senator Rand Paul, Republican of Kentucky, pitched a gathering of venture capitalists last week in an effort to show them that he may be the next big thing.

The session — sandwiched between start-ups selling things like liquid biopsies for cancer and a hangover remedy for people who have smoked too much marijuana — was organized with the help of Robert D. Leppo, an investor drawn to the senator’s libertarian views. Over a round of golf at the Ritz-Carlton Half Moon Bay last summer, Mr. Leppo urged Mr. Paul to reach out more aggressively to the moneyed corridors of Northern California.

“I said to him the idea of talking to angel investors’ forums would be a wonderful idea,” Mr. Leppo said. “My thinking was, let’s say you go to an angel forum where there’s 100 investors and each of them comes up with $10,000. That’s great for him.”

The senator last week talked up his plan for a 17 percent flat tax, a hit with the high-earning crowd. He also took questions on issues spanning the crisis in Crimea to abortion.