The morphology of galaxies provide us with a unique tool to connect and understand other related physical properties and their changes over the course of cosmic time. Only recently, thanks to big and/or deep surveys, we have access to a wealth of data for unprecedented number galaxies. The morphological catalogue of the OTELO survey galaxies detected in Hubble Space Telescope (HST)-ACS F814W images is presented. We explore various methods from previous works to separate early-type (ET) and late-type (LT) galaxies classified via spectral energy distribution (SED) fittings using galaxy templates. Together with this article we release the catalogue containing main morphological parameters in F606W and F814W bands derived for more than 8000 sources. The morphological analysis is based on the single-Sersic profile fit. The GALAPAGOS-2 software was used in order to provide multi-wavelength morphological parameters fitted simultaneously in two HST-ACS bands. GALAPAGOS-2 detects, prepares guess values for GALFIT-M, and provides the best-fitting single-Sersic model in both bands for each source. Stellar masses were estimated using synthetic rest-frame magnitudes recovered from SED-fitting of galaxy templates. The morphological catalogue is complemented with concentration indexes from a separate SExtractor dual, high dynamical range mode. A total of 8812 sources were successfully fitted with single-Sersic profiles. The analysis of a carefully selected sample of ~3000 sources up to z_phot=2 is presented in this work, from which 873 sources were not detected in previous studies. We found no statistical evidence for the evolution of low-mass end of mass-size relation for ET and LT since z=2. Furthermore, we found a good agreement on the median size evolution for ET and LT galaxies, for a given stellar-mass, with data in the literature. Compared to previous works on faint field galaxies, we found similarities regarding rest-frame colours, Sersic and concentration indices.