It's a play on words, a joke. "What time is it?" can be answered by all of the following:
"Time to go to work." or "8:30 - time to go to work."
"Time to get up."
"Time for lunch."
Answering with "Time to get a watch." is a joke because the person asking obviously doesn't have a watch if they need to ask someone what the time is, and especially if they ask often, it really is time for them to get a watch!