Can my employer give me a drug test?

So I am 16, and i just applied for a job that includes cleaning and possibly care for animals around a veterinarians office. I smoked weed like 8 days ago and don't plan on doing it again. But on my application, there was never anything that mentioned a drug test. Since it wasn't on my application, are they allowed to drug test me? and if so, will they do it right away? Thanks