We present the potential capability of the Murchison Widefield Array (MWA) in searching for pulsars and rotating radio transients (RRATs). The MWA, an array of 128 antenna tiles (each tile being a 4x4 dipole array) is a SKA (Square Kilometre Array) precursor which operates within the 80-300 MHz of the electromagnetic spectrum. The flux density of most radio pulsars tend to peak near or within the low frequency range in which the MWA operates. This along with its wide field of view makes the MWA an efficient instrument for conducting pulsar surveys, and we discuss some plausible survey strategies. Pulsar searches with the MWA will be sensitive to slow pulsars and RRATs, while maintaining reasonable sensitivity to millisecond pulsars. We also present some early pulsar detections with the MWA's high time resolution recorder currently under development.