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 .