This work initiates the study of a beyond-diagonal reconfigurable intelligent surface (BD-RIS)-aided transmitter architecture for integrated sensing and communication (ISAC) in the millimeter-wave (mmWave) frequency band. Deploying BD-RIS at the transmitter side not only alleviates the need for extensive fully digital radio frequency (RF) chains but also enhances both communication and sensing performance. These benefits are facilitated by the additional design flexibility introduced by the fully-connected scattering matrix of BD-RIS. To achieve the aforementioned benefits, in this work, we propose an efficient two-stage algorithm to design the digital beamforming of the transmitter and the scattering matrix of the BD-RIS with the aim of jointly maximizing the sum rate for multiple communication users and minimizing the largest eigenvalue of the Cramer-Rao bound (CRB) matrix for multiple sensing targets. Numerical results show that the transmitter-side BD-RIS-aided mmWave ISAC outperforms the conventional diagonal-RIS-aided ones in both communication and sensing performance.