While Juliet's age is explicitly stated as 13, Romeo's age is never officially revealed within the text. Most stage and movie renditions that I have seen put him as older than Juliet, but still in his teen years. His somewhat impulsive behavior and the rapidity with which he is able to transition from feelings for Rosaline to strong feelings for Juliet seem to indicate a high hormone level, which would be more consistent for a teenager than for someone in his early twenties.
While a 13-year-old bride might seem ludicrous in the modern age, we must remember that the life expectancy during Shakespeare's time was only about 30-35 years. People married far younger and started families far earlier in Shakespeare's day than they do at present.