  We report on electron spin resonance (ESR) studies of the spin relaxation in
Cs$_2$CuCl$_4$. The main source of the ESR linewidth at temperatures $T \leq
150$ K is attributed to the uniform Dzyaloshinskii-Moriya interaction. The
vector components of the Dzyaloshinskii-Moriya interaction are determined from
the angular dependence of the ESR spectra using a high-temperature
approximation. Both the angular and temperature dependence of the ESR linewidth
have been analyzed using a self-consistent quantum-mechanical approach. In
addition analytical expressions based on a quasi-classical picture for spin
fluctuations are derived, which show good agreement with the quantum-approach
for temperatures $T \geq 2J/k_{\rm B} \approx 15$ K. A small modulation of the
ESR linewidth observed in the $ac$-plane is attributed to the anisotropic
Zeeman interaction, which reflects the two magnetically nonequivalent Cu
positions.
