I don't have the pattern handy, but you would need to analyze what sort of properties the silk lends to the garment. Is it softness? Drape? You could posisbly substitute a yarn like Classic Elite Premiere, which is a blend of Pima Cotton and Tencel. Very soft and drapes well. Mercerized cottons have a crisp finish, which may or may not lend the sort of qualities you're looking for.
For future reference, if you're interested in sustainable resources, avoid buying acrylic yarns. Acrylic is made from plastic, and unless it's a recycled yarn (which are expensive and difficult to find), is made from non-renewable petroleum.