There is currently no melee-specific class in Diep.io but you can definitely try this class and stat combination if you want to try your hand at using Body Damage to demolish your foes.
If you want to go melee, your best bet is going with the Destroyer tank class. The Destroyer (Machine Gun -> Destroyer) is the slowest-firing of all the tanks, but seems to have higher base health (or defense? who knows) than the other classes. This is what makes the Destroyer the best option for melee.
If you want you can also go Twin Flank (Twin -> Twin Flank) if you want to go melee, but the Twin Flank's base health/defense is low, meaning it can't take as much damage as the Destroyer. When going melee, the longer you can survive the better -- because you also take damage when you go in to damage another player.
Destroyer melee means you will live longer. Twin Flank means you will move fast, but have a tougher time staying alive.
When going melee, you always want to shoot away from the direction you're moving so you will go faster.
The stats make the tank in Diep.io and if you want to try to be a body-ramming powerhouse you need to distribute your stat points differently than if you were going with a shooting build.
Your most important melee stats are:
Health Regen makes your health recover faster, which means you'll be back in action more quickly once you take damage.
Max Health means you can take more damage, which is a must have for melee.
Body Damage means you'll do more damage when you ram your body into other players and food. It is your primary damage stat when going melee.
Movement Speed lets you not only get away from dangerous situations faster (which is important when leveling) but also chase down other players easier.
Focus on Health Regen and Max Health over Body Damage and Movement Speed at early levels, but put 2 or 3 points into Body Damage early to farm more easily.
If you're having to dodge a ton of enemy bullets, invest a few points in Movement Speed Early.
After you've maxed out all 4 stats, put the rest in Reload to shoot faster, which makes you move faster due to bullet recoil.
It isn't too hard to get high on the leaderboards using a melee build, especially using the Destroyer class. Going melee is harder than a standard shooting build, but there's a certain satisfaction that comes from swooping in on the highest ranked player and ramming them dead in two shots.