In a typical communication system, in order to maintain a desired SNR level, initial beam alignment (BA) must be established prior to data transmission. In a setup where a Base Station (BS) Tx sends data via a digitally modulated waveform, we propose a User Equipment (UE) enhanced with a Hybrid Intelligent Reflecting Surface (HIRS) to aid beam alignment. A novel multi-slot estimation scheme is developed that alleviates the restrictions imposed by the Hybrid Digital-Analog (HDA) architecture of the HIRS and the BS. To demonstrate the effectiveness of the proposed BA scheme, we derive the CRLB of the parameter estimation scheme and provide numerical results.