You might be able to become a substance use counselor if you have a felony conviction, but it's not guaranteed because the rules differ by state. It's not uncommon for people in recovery from substance use disorder to become counselors themselves. The process may be harder with a felony conviction, which will require explanation during a background check. It helps to demonstrate a period of rehabilitation since the conviction, including steady work and education. You may be granted a contingent license until you've passed a certain period of supervision.
The ATTCN gives details on regional licensure rules around the country, including rules for candidates with criminal records.