  The quantum-spin S = 1=2 chain system Cs$_2$CuCl$_4$ is of high interest due
to competing anti-ferromagnetic intra-chain J and inter-chain exchange J'
interactions and represents a paramount example for Bose-Einstein condensation
of magnons [R. Coldea et al., Phys. Rev. Lett. 88, 137202 (2002)]. Substitution
of chlorine by bromine allows tuning the competing exchange interactions and
corresponding magnetic frustration. Here we report on electron spin resonance
(ESR) in single crystals of Cs$_2$CuCl$_{4-x}$Br$_x$ with the aim to analyze
the evolution of anisotropic exchange contributions. The main source of the ESR
linewidth 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. The obtained results support the site selectivity of the Br
substitution suggested from the evolution of lattice parameters and magnetic
susceptibility dependent on the Br concentration.
