Yes—this is essentially mosaic/panorama stitching for a flat subject. A good open-source option is Hugin. For this kind of project, the key is using settings appropriate for a flat surface and camera movement between shots; in Hugin, that means using an optimizer mode such as positions and translation rather than a normal distant-scene panorama setup.

Another free option is Microsoft ICE, which can also stitch overlapping images automatically.

If you need maximum precision, especially for professional output, manual assembly in Photoshop may be the most accurate approach, though it is much more time-consuming than automatic stitching.

Practical tip: shoot with plenty of overlap between frames and keep lighting and exposure consistent to help any stitcher align the images cleanly.