The Republican National Committee, together with President Donald Trump’s re-election campaign, raised more than $53 million in the first quarter of 2017, according to party and campaign officials, fueled by the same class of online donors who flocked to Mr. Trump last year.

Of that, the RNC raised $41.3 million in the first three months of the year—more than double what its Democratic counterpart raised in the quarter after former President Barack Obama was elected in 2008—while Mr. Trump’s campaign raised $3.3 million and...