Yes, restaurants are required to withhold federal taxes if your earnings are high enough. The reason they often don't is that the amount that they pay you, not including tips, is usually very low.
In addition, they sometimes allocate tips to you based on the total sales volume at the restaurant. To help you with that issue, you can keep your own records and report your own tips to the restaurant. Follow this link for more about that.
If you are working at a restaurant, you can give them a new W-4 form and use line 4(c) to order them to withhold a flat amount from each paycheck. Follow this link to complete a new W-4 form.