If you're convicted of burglary, you can still get federal financial aid for college. But current rules make it nearly impossible for tens of thousands of students who are charged for even minor drug offenses to get that same aid.

That's because the Free Application for Federal Student Aid, which was released on Tuesday for the 2020-2021 school year, includes a question: Have you been convicted for the possession or sale of illegal drugs for an offense that occurred while you were receiving federal student aid (such as grants, work-study or loans)?

If students answer "yes," their eligibility for aid will be restricted until they complete a drug rehabilitation program or pass two random drug tests. During the 2003-2004 school year, roughly 41,000 students, or about .03% of those who filled out the FAFSA application, were deemed ineligible for aid on the basis of drug-related offenses, according to perhaps the most comprehensive report on the topic issued by the Government Accountability Office in 2005.

"As we rethink the war on drugs and the convictions and prison sentences that came with it, we must address all aspects that impacted our communities," Rep. Karen Bass (D-Calif.) said in a statement Tuesday. "Investing in a person's education is perhaps the best investment we can make to ensure our young people succeed."

That's why the congresswoman, along with over 30 co-sponsors, is introducing the Financial Aid Fairness for Students Act on Tuesday, which would prohibit the Department of Education from asking about drug convictions in future federal aid applications, including the FAFSA.

The legislation would repeal sections of the Higher Education Act that suspends college aid for any person convicted of a drug offense, a barrier that Bass says has "denied tens of thousands of people of needed aid for college and has discouraged tens of thousands of others from even applying."

"This bill addresses yet another unnecessary hindrance for folks trying to access higher education," Bass tells CNBC Make It. "Higher education is not accessible right now. How do you expect people to turn their lives around if you don't give them tools not only not give them tools, but don't give them access to tools to do so?"

Under the current rules, if a student is convicted of drug possession, they face one year of ineligibility from the time of their first conviction. A second conviction earns them two years of ineligibility, while a third offense will suspend their eligibility for financial aid indefinitely.

During the 2016-2017 school year, over 1,000 students were deemed fully ineligible because they had a drug-related conviction or failed to properly answer the question, according to Insider Higher Ed's analysis of data from the Department of Education. The Education Department deemed another 250 students partially suspended from receiving aid.

"This policy unfairly targets poor and minority students and costs society more in terms of crime and lost economic productivity," Rep. Danny Davis (D-Ill.), co-sponsor of the FAFSA Act, said regarding the current FAFSA question around drug convictions.

Graham Boyd, director of the ACLU's Drug Law Reform Project also called the policy "discriminatory." While the FAFSA does not collect data on students' race, and researchers are therefore unable to conclusively say how minority groups are affected, African Americans and Latinos are arrested and convicted of drug offenses at higher rates than white Americans.

"If a student is convicted of a drug offense and her family can afford to pay for college, she will be unaffected by the legislation, while those who are already in danger of being forced to society's margins will be further disempowered," Boyd said.

And advocates say that in addition to presenting an incomplete picture on how the policy affects minorities, the Education Department's data does not capture the number of students who failed to even apply for aid because they feared they would be ineligible. In fact, last year, 38 advocacy groups joined together and sent joint letters urging leaders of the U.S. Senate Committee on Health, Education, Labor & Pensions and U.S. Secretary of Education Betsy DeVos to eliminate the FAFSA's drug conviction question.

The letters noted that the Center for Community Alternatives found in a 2015 report that nearly two out of every three undergraduate applicants to the State University of New York who disclosed a felony conviction never completed their application.

This is not the first time lawmakers have pushed to provide students with drug convictions increased access to federal financial aid. Rep. Bill Foster (D-Ill.) re-introduced the Second Chance for Students Act in July, which would give students convicted of marijuana possession a break before they lost their financial aid.

"Education promotes economic well-being and labor force participation," Davis says. "Excluding individuals who have struggled with addiction from financial assistance is an ineffective policy that has harmed tens of thousands of students."

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Lawmakers want to give students with drug convictions access to financial aid - CNBC