We present the results from the optical component of a survey for damped Lyman- \alpha systems ( DLAs ) towards radio-loud quasars . Our quasar sample is drawn from the Texas radio survey with the following primary selection criteria : z _ { em } \geq 2.4 , optical magnitudes B \leq 22 and 365 MHz flux density S _ { 365 } \geq 400 mJy . We obtained spectra for a sample of 45 QSOs with the William Herschel Telescope , Very Large Telescope and Gemini-North , resulting in a survey redshift path \Delta z = 38.79 . We detect nine DLAs and one sub-DLA , with a mean absorption redshift \langle z \rangle = 2.44 . The DLA number density is n ( z ) = 0.23 ^ { +0.11 } _ { -0.07 } , in good agreement with the value derived for DLAs detected in the Sloan Digital Sky Survey at this redshift . The DLA number density of our sample is also in good agreement with optically-complete radio-selected samples , supporting previous claims that n ( z ) is not significantly affected by dust obscuration bias . We present N ( H i ) column density determinations and metal line equivalent width measurements for all our DLAs . The low frequency flux density selection criterion used for the quasar sample implies that all absorbers will be suitable for follow-up absorption spectroscopy in the redshifted H i 21 cm line . A following paper ( Kanekar et al . ) will present H i 21 cm absorption studies of , and spin temperature determinations for , our DLA sample .