Why not? There’s nothing that requires Catholics to make resolutions at the start of the New Year, however, we do seem to be a religion that holds this practice in high regard.
Each time we go to confession we “firmly resolve with the help of God’s grace” not to sin again. We renew the promises we made at baptism during the Easter Vigil and at other times. We make a public display of making some kind of resolution at Lent as well.
So my advice is that while we don’t have to do this at New Year’s, perhaps we can use this period of time as a warm-up for Lent. We should think about something that we might want to give up that is seriously unhealthy for us and begin to make a plan for the 40 days of Lent. This way, we take the time to discern what we really want to change instead of superficially jumping into a resolution that really doesn’t change much in our lives.