A 3.9 GPA is above Tuskegee's admitted middle-50% GPA range of 3.3–3.75.
You're competitive on GPA — at a school this selective the rest of your application (rigor, essays, extracurriculars, and spikes) is what decides it.
A GPA is the single biggest academic factor, but it's necessary, not sufficient — especially at a 48.7%-acceptance school like Tuskegee. Your test scores, course rigor, extracurriculars, essays, and any standout achievements all move the number. The estimate above assumes typical scores and rigor; your real odds depend on your full profile.
Estimates are CDS-based and for a typical applicant. Run your full profile for your real, calibrated odds.