Potentially, yes. In order to buy a marketplace plan, you must have a qualifying immigration status, such as permanent residency (green card), certain types of visas, or refugee status. You can find more information about qualifying statuses here.
If you are not a U.S. citizen, a U.S. national, or are not lawfully present status in the U.S., you are not eligible to buy a plan on the health insurance marketplace. However, you can shop for individual health insurance outside of the marketplace. To obtain coverage, contact a state-licensed health insurance company or a licensed agent or broker. Your state Department of Insurance can help you find one. (45 C.F.R. § 155.305).
Note that in October 2018, the Trump Administration proposed an expansion to the current policy that determines whether certain immigrants would be considered a “public charge.” While the rule is not finalized, it may eventually impact individuals seeking admission to the U.S. or seeking to adjust status to lawful permanent residence (green card) applying for or using certain public benefits, like Medicaid. Under current and proposed rules, the application and use of premium tax credits and cost-sharing reductions are exempted from the public charge determination test. If the rule is finalized, you will have time to act before the rule goes into effect, and thus can still apply for and use public benefits including Medicaid in the interim.