Arvind Kejriwal burst into Indian politics four years ago by organizing a high-decibel anticorruption movement that promised to clean up public life. But even though he was elected in a landslide victory last February to lead the Delhi city government, in many ways the 47-year-old activist-turned-politician has already lost his sheen.

Since his election, Mr. Kejriwal’s most credible comrades in the anticorruption movement—which morphed into a political party back in 2012—have become his biggest critics. He shows no talent...