We studied the X-ray timing and spectral variability of the X-ray source Sw J1644+57, a candidate for a tidal disruption event. We have separated the long-term trend (an initial decline followed by a plateau) from the short-term dips in the Swift light curve. Power spectra and Lomb–Scargle periodograms hint at possible periodic modulation. By using structure function analysis, we have shown that the dips were not random but occurred preferentially at time intervals ≈(2.3, 4.5, 9) × 105 s and their higher order multiples. After the plateau epoch, dipping resumed at ≈(0.7, 1.4) × 106 s and their multiples. We have also found that the X-ray spectrum became much softer during each of the early dips, while the spectrum outside the dips became mildly harder in its long-term evolution. We propose that the jet in the system undergoes precession and nutation, which causes the collimated core of the jet briefly to go out of our line of sight. The combined effects of precession and nutation provide a natural explanation for the peculiar patterns of the dips. We interpret the slow hardening of the baseline flux as a transition from an extended, optically thin emission region to a compact, more opaque emission core at the base of the jet.