Quoting the nearby information board:
In 1321 King Robert Bruce granted the lands of Sauchie to Henri de Annand, Sheriff of Clackmannan. Mary de Annand, his descendant, married Sir James Schaw of Greenock in 1531. He probably built the Sauchie Tower soon after the marriage. The Schaws were one of the most influential families in mediaeval Scotland and in c1460 Sir James’ son became Governor of Stirling Castle.