When Rep. Paul Ryan in July announced new proposals to fight poverty, he may have also found a way to settle the debate about raising the minimum wage. His plan to expand the Earned Income Tax Credit for childless adults would boost take-home pay and fix a hole in the social safety net without hurting jobs. That’s a compromise that Democrats and Republicans can support.

President Obama wants to raise the minimum wage to $10.10 from $7.25. But the Congressional Budget Office released a report in February estimating that this higher wage would eliminate 500,000 jobs. For the past five months, proponents of the president’s proposal have been working to rally public opinion. The labor union-backed group Americans United for Change launched a nationwide bus tour this spring to promote the wage hike. Last month, a coalition of more than 60 advocacy organizations kicked off a public challenge to live on the federal minimum wage for a week.

Many Democrats plan to make the minimum wage an issue to boost voter turnout in the midterm election and have no interest in negotiating the $10.10 figure. Others seem more inclined to compromise: West Virginia Democrat Sen. Joe Manchin, for instance, told MSNBC in May that he’s “willing to sit down and talk about anything that’ll raise” the minimum wage above $7.25.

But even a modest wage increase would have immodest consequences. Increasing the minimum wage to $9 an hour would cost roughly 100,000 jobs, according to CBO estimates.

Enter Mr. Ryan’s proposal. The EITC, a refundable tax credit for low-income households that phases out as income rises, helps the working poor without imposing a harmful mandate on employers. But the EITC has one major weakness: Under current law, the size of the credit is dramatically smaller for individuals and families without children.

For instance, a single mother with two children who works part time for the federal minimum wage receives nearly $4,500 in additional income from the EITC. That’s a 40% increase in take-home pay, bumping her hourly wage to $10.15 an hour from $7.25. But a single woman without children who works the same hours for the same wage takes home $265 in EITC benefits annually—a 2% increase in take-home pay.

Mr. Ryan’s plan would close that gap. His proposal, as described in a House Budget Committee draft, would double the credit that childless adults receive as a percentage of their eligible income—to 15.3% from 7.65%. It would also lower the age of eligibility to 21 from the current 25, and raise the income threshold for receiving the maximum credit to $11,500 from $8,220. The results are significant: A childless adult who now receives $265 annually would take home $1,005 a year under Mr. Ryan’s plan. That’s roughly the equivalent of raising their minimum wage to $8 an hour.

It’s not just good politics; it’s good policy. Mr. Ryan’s proposal would reach childless adults in poverty whose hourly wage nevertheless exceeds $10.10. (A 2010 study in the Southern Economic Journal, sponsored by the Employment Policies Institute and conducted by economists Joseph Sabia and Richard Burkhauser, found that 25% of hourly employees in poverty earn $12 an hour or more.) It also circumvents another problem with using an increase in the minimum to reduce poverty: Only 18% of the benefits from Mr. Obama’s wage proposal would go to minimum-wage earners living in poor families, as David Neumark explained in these pages last month.

A direct payment from the IRS, on the other hand, goes straight to its intended beneficiaries.

The EITC program has its share of flaws. A 2014 report by the Treasury inspector general for tax administration estimated that up to 26% of the program’s payments in fiscal 2013 were made in error. Mr. Ryan’s proposal also acknowledges the problem (not unique to the EITC) of marginal tax rates, where the loss of benefits from safety-net programs creates perverse incentives for low-wage earners.

Coping with these challenges means improved enforcement strategies for the IRS and perhaps a slower phaseout rate for the EITC. But an imperfect partial subsidy that rewards work is still preferable to the jobs lost as a consequence of a higher minimum wage.

Mr. Ryan’s plan is a better solution and a win for both sides of the aisle. Democrats can point to a progressive tax policy that provides substantial gains for low-income workers, and Republicans can boast of raising wages without burdening employers.