WASHINGTON—In a swift victory for tea-party activists, the Senate's top Republican agreed Monday to a plan to ban GOP members from proposing earmarks for spending bills, suggesting that what was once a core part of legislating has now become politically unacceptable.

Earmarks, or spending items tucked into legislation by individual lawmakers, had long been defended by leading Republican and Democratic lawmakers. The development came as Sen. Mitch McConnell, the Senate Republican leader, reversed his longstanding support for...