They would be called a "bowman" meanwhile an expert of archery is sometimes known as a toxophilite.
I don't personally do it but I really admire it, people who are experts in it are called toxophilites.
I recently took up archery and I think I love it. Do you know anything about Archery? Archery is a sport/skill of using a bow to propel arrows. And a great sport it is. Do you know where archery originated from? I do not know that it was invented at minimum 10000 years ago, and has been used for military and hunting. Wow, thats amazing. Its been around for a long time. Do you know which culture invented it? I don't know the culture, just that it was around the transition period of the Upper Paleolithic to Mesolithic times, An I guess it has spread out through out all the different cultures. Which type of bow do you consider to be the best? I don't have a stance on that and did you know that there are no definite early bows? There were pointed shafts but could have been thanks to spear-throwers. So we don't have any evidence of bows themselves, interesting! Do you happen to know what a person doing archery is called?
A person who participates in archery is typically called an archer or a ''bowman'', and a person who is fond of or an expert at archery is sometimes called a toxophilite.