We construct an effective action for QCD by expanding the quark determinant in powers of the chemical potential at finite temperature in the case of massless quarks. To cut the infinite series, we adopt the Weinberg power counting criteria. We compute the minimal effective action (similar to p(4)), expanding in the external momentum, which implies the use of the hard thermal loop approximation. Our main result is a gauge invariant expression for the phase theta of the functional determinant in QCD and recovers dimensional reduction in the high-temperature limit. We compute, analytically, in the range of p << 2 pi T, including perturbative and nonperturbative contributions, the latter treated within the mean field approximation. Implications for lattice simulations are briefly discussed.