We consider the problem of single snapshot direction-of-arrival (DOA) estimation of multiple targets in monostatic multiple-input multiple-output (MIMO) radar. When only a single snapshot is used, the sample covariance matrix of the data becomes non-invertible and, therefore, does not permit application of Capon-based DOA estimation techniques. On the other hand, low-resolution techniques, such as the conventional beamformer, suffer from biased estimation and fail to resolve closely spaced sources. In this paper, we propose a new Capon-based method for DOA estimation in MIMO radar using a single radar pulse. Assuming that the angular locations of the sources are known a priori to be located within a certain spatial sector, we employ multiple transmit beams to focus the transmit energy of multiple orthogonal waveforms within the desired sector. The transmit weight vectors are carefully designed such that they have the same transmit power distribution pattern. As compared to the standard MIMO radar, the proposed approach enables transmitting an arbitrary number of orthogonal waveforms. By using matched-filtering at the receiver, the data associated with each beam is extracted yielding a virtual data snapshot. The total number of virtual snapshots is equal to the number of transmit beams. By choosing the number of transmit beams to be larger than the number of receive elements, it becomes possible to form a full-rank sample covariance matrix. The Capon beamformer is then applied to estimate the DOAs of the targets of interest. The proposed method is shown to have improved DOA estimation performance as compared to conventional single-snapshot DOA estimation methods.