Well, it's your money, but I'd try to patch it with something like duct tape. Since it is the middle of the tread,it isn't as likely to blow out catastrophically as a cut on the side wall might. But a lot depends on the construction of the tire.

Maybe if you rephrased your question as "How do I fix a tire with a small cut in the middle of the tread?"; and post it on the bike mechanics forum you might get some better advice. People on that forum like to fix things. You could also use the search function, and read about tire cuts. There must be hundreds of threads concerning the subject.

One thing I've observed over the years on these forums is that if you ask a question such as "Should I do A or B?"; you'll get 10 votes for A and 10 votes for B.