Is it legal for a company to ask a male American Indian to cut his hair based on their dress code?

As a general matter--yes. Companies have enormous discretion in setting dress codes, so long as they do not discriminate against people on the basis of sex, race, religion, age over 40, or disability, in doing so. The fact that the employee is a male Native American does not make this discriminatory as long as he being held to the same standards or dress code as other male employees (there may be different standards, such as for hair length, for men and women, since United States society at large recognizes different ways of dressing for the two sexes, etc.).

If the male Native American is being held to a different standard than other male employees, however, that would be discrimination.

If the male Native American's hair length is related to his religious observances (the way, for example, Sikhs and Orthodox Jews have specific, religiously based hair styles), however, they might be required to accomodate the length, at least so long as it can be done without impairing safety (e.g. if the man works around heavy machinery, they may be allowed to require him to cut his hair even if he has a religious basis for its length, to avoid having it caught in the machinery).