Yes! Sunscreen can and should be applied to any exposed skin of any age, even an infant. Of course, it’s best to avoid the sun, especially during peak sun hours, so go for a walk or swim with your little one early in the morning or late in the day. Always cover your children with a wide brimmed hat, light weight SPF clothing (long sleeve shirts and long pants preferred) and use an SPF sun shade on your stroller (attach to your stroller so baby is completely shaded). You can also wash sun protection into your child’s clothing with a product like Sun Guard Wash-in Protection. It gives clothing a protective factor of 30 for up to 20 washes.
When choosing a sunscreen for your infant or toddler, use an SPF of at least 30, with UVA/UVB protection or "broad spectrum" protection and "water resistant". Test a small amount on your child's skin to make sure there is no reaction. Most importantly, reapply often (every 2 hours or after swimming or sweating) and use lots.