We present a modular multichannel acquisition system for high-resolution X-ray spectroscopy detectors. The system has been developed for the acquisition of signals coming from 12-element Si drift detectors but can be easily used for the acquisition of signals coming from other kinds of detectors. The main characteristics of the system are flexibility and low cost. The basic component of our acquisition system is a board that acquires the signal coming from a shaping amplifier and provides peak stretching, peak detection, and analog-to-digital conversion. The converted data are transferred to the PC using the protocol of a bidirectional enhanced parallel port. The acquisition system has been fully developed and tested. The obtained overall linearity is within + / - 0.4%. The achieved energy resolution is fully comparable to that achieved with a commercial multichannel analyzer system equipped with a 13-bit analog-to-digital converter. The system has been extensively used to acquire signals coming from single- and multi-element silicon drift detectors.