We present the first results of the angular auto-correlation function of the galaxies detected by the Infrared Array Camera (IRAC) instrument in the First Look Survey (FLS) of the Spitzer Space Telescope. We detect significant signals of galaxy clustering within the survey area. The angular auto-correlation function of the galaxies detected in each of the four IRAC instrument channels is consistent with a power-law form \(w(\theta)=A\theta^{1-\gamma}\) out to \(\theta = 0.2\arcdeg\), with the slope ranging from \(\gamma = 1.5\) to 1.8. We estimate the correlation amplitudes \(A\) to be \(2.95 \times 10^{-3}\), \(2.03 \times 10^{-3}\), \(4.53 \times 10^{-3}\), and \(2.34 \times 10^{-3}\) at \(\theta=1\arcdeg\) for galaxies detected in the IRAC 3.6\(\mu\)m, 4.5\(\mu\)m, 5.8\(\mu\)m, and 8.0\(\mu\)m instrument channels, respectively. We compare our measurements at 3.6\(\mu\)m with the previous K-band measurements, and discuss the implications of these results.