Is there a tutorial in Terraria? If so, How do I start it?

The PC version of Terraria does not have a distinct tutorial

As more-or-less a sandbox game, Terraria does not have a formalized tutorial. The keyboard controls can be viewed and customized in the menu, but other than that, it's expected for a player to learn most of the basics simply through experimenting while playing the game. Still, there are two main sources of information about Terraria.

The Guide

When you first enter a new world, you'll see another person walking around the landscape nearby. This NPC is the Guide, who can provide useful information for new players, as well as lists of items that can be crafted from materials you have. You can talk to him by right-clicking him while you are standing close to him.

The Wiki

Once you're a bit more experienced with the game and have progressed some, the advice given by the Guide will start to be less useful, and eventually he will stop providing new information at all. By this point, you should probably be familiarizing yourself with The Official Terraria Wiki, where you can find lots of helpful information about every item, enemy, NPC, and event in the game. Do be wary of looking around too much, as much of the fun of a sandbox game like Terraria is in discovering new things on your own, but how much you follow that advice is up to you.

As mentioned by Mani5556, the Wiki also has a Getting Started guide, which should be helpful to a new player.

But the Console and Mobile versions do

According to Joishi Bodio and CodeMoose, the console and mobile versions of Terraria do have a tutorial world, apparently consisting of a small, predetermined world on a floating island. The player is given various instructions on the controls and how to perform basic tasks such as mining and constructing a house for NPCs, before being recommended to create a normal world. More information about the tutorial can be found on the Wiki, though it doesn't include the actual information from the tutorial, only a summary.

I have a little addition to Mike Kellogg's answer and since it seems like I can't comment yet, due to lack of reputation, I will put it as a separate answer.

Terraria itself doesn't have a tutorial as Mike's answer said, but what it does have is In-Game-Achievements, which will help you getting started and which will lead you through the progression of the game and the order of the bosses. You can't call it a tutorial, but it's a hint on what to do first and where to go from that.