Kazuma Ieiri’s campaign trail began with a tweet. “I will run for the Tokyo governor election if this tweet gets retweeted 1,000 times,” the 35-year-old star entrepreneur posted on his Twitter account in December. It took only 30 minutes for him to gather enough support. Many celebrities, including famous entrepreneur Takafumi Horie, joined in. Mr. Ieiri, one of the youngest Tokyo governor candidates ever, hadn’t been involved in politics before his December tweet, but he’s drawn a following online over the years, especially after he became the youngest manager to list his company on JASDAQ when he was 29. While running several internet-service companies and restaurants, Mr. Ieiri has also been active on Twitter, occasionally asking his followers to donate money to various causes. Most recently, he helped a mother to raise the cost of a delivery through twitter — “cloud birthing funding,” he called it.