As TypeIA pointed out, the wrong form of "invigorate" is used here. Invigorate is a verb, and in this sentence it is used as if it were an adjective. Changing the word to "invigorating" gives us this sentence, which is grammatically correct:
The aroma of the invigorating morning cup of tea comes wafting up the stairway and soon I am sipping it slowly and reverentially without rushing.
It should be noted that, while this new sentence is grammatically valid, it still has what is almost certainly an error; "it," the object of "sipping" in the second clause, refers to the subject of the first clause, "aroma." It is very likely the author meant they were sipping the tea, but the sentence states that they are sipping its aroma.