We present ESR, x-ray diffraction and dilatometry studies in a La_7/8Sr_1/8MnO₃ single crystal. ESR experiments were performed in the paramagnetic regime (T_C ~ 180 K), from 220 K to 570 K at a microwave frequency of 9.4 GHz. We measured the ESR linewidth as a function of temperature with the static magnetic field (H) parallel to the crystallographic directions [100] and [001], referred to the orthorhombic (Pbnm) axes. Detailed angular variations at constant temperature for H rotating in the (001), (010) and (-110) planes were also performed. The temperature dependence of the linewidth for fixed directions clearly reflects the changes in the symmetry of the crystal. At the Jahn Teller (JT) transition, a very noticeable decrease of the linewidth is observed. The angular dependence of the linewidth reveals an anisotropy that is temperature dependent. The amplitud of the variations decreases with T and almost dissapears above T_JT ~ 280 K. However, there is a small remnant anisotropy present up to 400 K. We have carefully investigated the temperature dependence of this anisotropy across the Jahn-Teller transition. We showed that it is related with the evolution of the crystal field interactions. The symmetry of the ESR spectra is explained in terms of a spin Hamiltonian that includes isotropic Heisenberg superexchange, single ion-crystal field, and Dzyaloshinsky-Moriya antisymmetic exchange. The experimental angular variation of the ESR linewidth and its temperature dependence were fitted using the calculated expression for the linewidth as obtained from a perturbative Kubo-Tomita approach. From the ESR data we have obtained a ratio E/D = -0.4 for the spin Hamiltonian coefficients associated with the orthorhombic (E) and tetragonal (D) Jahn-Teller distortions of the MnO₆ octahedra. The temperature dependence of the parameters of the model are presented, and the correlation with the dilatometry results are discussed.