Can a foreign-born person who enlisted in the Army get a security clearance?

S Mmm - Per Executive Order 12968 Section 2.6(a) - Access by Non-United States Citizens. Where there are compelling reasons in furtherance of an agency mission, immigrant alien and foreign national employees who possess a special expertise may, in the discretion of the agency, be granted limited access to classified information only for specific programs, projects, contracts, licenses, certificates, or grants for which there is a need for access. Such individuals shall not be eligible for access to any greater level of classified information than the United States Govern-ment has determined may be releasable to the country of which the subject is currently a citizen, and such limited access may be approved only if the prior 10 years of the subject's life can be appropriately investigated.

I would see a recruiter and apply for the position you are interested in. I would guess each person differs in what clearance level they qualify for depending on their situation. Congratulations on your decision to join.

The answer isn't going to change, no matter how many times you ask it. Until and unless you are a citizen, you will not get a clearance. And even then, there are no guarantees. Plenty of US citizens are denied, or lose, their clearance, every year. I applaud your desire to serve. If intel is the only thing you're interested in, get cracking on your citizenship and try. No one here will be able to give you a definitive answer. I would point out that there are many other ways you could serve, if this one doesn't work out.