How can I thicken tea?

You could try using arrowroot. This is a widely available alternative to cornstarch - it is used in cookery because it doesn't turn liquids cloudy like cornstarch does. In your case, it might work better as it also has a more neutral flavour.

Substitute 2 tbsps of arrowroot for 1 tbsp cornstarch, and make a slurry with cool water as you would cornstarch. One issue is that overheating can break down the arrowroot, preventing it from thickening, so you are probably better off adding it to the tea after removing it from the heat.

I'm going to recommend trying something a little bit different - instead of "thickening", I think what you really want is "body", which is similar, but different sensation. To get the mouth-feel I think you are after, you should try a complex sugar, like maltodextrin.

Maltodextrin is a complex carbohydrate, made from starch and composed of many sugar molecules, that is too large to be tasted as sweetness by the tongue, but adds some of the "texture" of sugar. It is used in energy drinks and homebrewed beer to add body and carbs, without adding much sweetness.

Start with 1% by weight added to the tea, and see how it works. Typical amounts for brewing are 0.5% (3.2 ounces/5 gallon batch) to 2% (12 ounces/5 gallon batch), with 1.25% (8 ounces/5 gallon batch) being the most common recommended value for people experimenting.

For you, for a pot of four 6 oz. servings of tea (24 ounces/680mL), about 0.24 oz (6.8g) of maltodextrin would be a good place to start. That would be roughly two teaspoons, depending on the density of your maltodextrin.

You can buy maltodextrin at "fitness nutrition" stores (bodybuilders use it for making special nutrient gels) and home brew stores. Midwest Supplies has maltodextrin for under $2.

Unflavored gelatin would likely work for you. It's available in most grocery stores. I'm not sure the ratio you'd want, but 1/4 oz. unflavored gelatin into 1/2 gallon (!) tea should have some effect. Also, drug stores now sell stuff that thickens liquids under names like Nectar-Thick. The stuff isn't cheap, but it's not horrifically expensive either. It should be able to thicken tea.

the cornstarch will always give this taste upon cooking it for a little time (5 min), it requires min around 20 min to be cooked, which will make your tea too thick, it is not recommended.

Instead of thickening your tea, why don't you buy a tea that brews a thicker liquor?

Some oolong teas such as 'Tieguanyin' is already more thicker than a green or black tea. If you want a real thick tea soup then go for a 'ripe pu erh'.

I'm not sure if this is thick enough for you but you can give it a try, and still add some thickener.

Powered sugar, soon after boiling. I wouldn't consider cornstarch for my drink over powered sugar, though I hear it contains 3% cornstarch, sounds like a great give and take to me. I use it for my chai:)