美味means delicious, but we don't necessarily use that word to describe a cup of tea. "這杯茶很好喝" will be a more suitable answer.

好吃，香，can express delicious

While that sentence is perfectly fine in English, Chinese don't say it that way. If you've tasted Chinese tea, you'd understand why. People drink Chinese tea for the aroma/smell and the unique taste. Edi has provided you with a good translation, Jack, Nina and others have explained further that we don't use "delicious/好吃" to describe tea. 好吃 is used mainly to describe food.

Specially for tea.... "This tea is delicious!" - direct translation would be as others had mentioned earlier. However, natives would usually say "这是好茶" which translates back as "This is good tea". It is just like "hello" being translated as "吃了飯嗎" Have you eaten your rice yet? It's just cultural preferences. For others, 好味道, 味道好, 好吃, etc will suffice.

我看到一家蛋糕店的招牌写：“delicious“同时用中文写”帝丽雪斯“，我想这单词是”美味的“意思。但是说tea ,不用这个单词。说cake常用这个词。