The astrologer is portrayed as a man who has always had to live by his own wits and on his luck. He pretends to be a learned astrologer, but

He was as much a stranger to the stars as were his innocent customers.

The moral of "An Astrologer's Day" seems to relate to the fact that the protagonist does not rely on the hocus-pocus of the pseudo-science of astrology with its useless paraphernalia, but on his own perception, intuition, and practical experience. If he knew more about astrology, he would be handicapped. When he runs into Guru Nayak, he talks a lot about the messages he supposedly reads in the stars, but he is only using the stars to befuddle his nemesis. The reader can see quite clearly that the astrologer is talking about the stars but really using his own practical knowledge to get himself out of a tight spot with a man who would kill him if he recognized him as the man he was searching for.

The best expression of the moral of the story may be the principle expressed by Laurence Sterne, author of the classic novel Tristram Shandy. 

An ounce of a man's own wit is worth a ton of other people's.

In the story "An Astrologer's Day," the protagonist's nemesis Guru Nayak is not relying on his "own wit." He is going from one astrologer to another, believing one of them will be able to answer his question, "Where can he find the man who tried to kill him in his village years ago?" Guru Nayak's quest is futile. How could anyone read the answer to that question in the stars? One after another, the astrologers send him on wild goose chases until, just by accident, Guru Nayak runs into the very man he has been looking for, although he doesn't recognize him.

The astrologer is versatile and adaptable. He has had to learn by experience. That is perhaps the main advantage of relying on your own perception, intuition, experience, and "street smarts."

Is there a moral of the story of "An astrologer's day"?I mean do we have anything to learn from this story?

It seems to me that the author is essentially trying to show how difficult it is for many people to survive in India, especially in the big Indian cities. The astrologer in this story actually has a good day, in spite of the dangerous foe he encounters. He brings home more money than usual--but more money than usual is not very much. His wife is delighted. 

"Twelve and a half annas," she said, counting. She was overjoyed. "I can buy some jaggery and coconut tomorrow. The child has been asking for sweets for so many days now. I will prepare some nice stuff for her."

The astrologer started work around noon and hasn't gotten home until nearly midnight. With all his effort he has only managed to acquire enough small coins for food plus a little extra treat for their daughter. What happens when he has a bad day? They have torrential rains in India. There must be days when nobody goes to the park. The astrologer may go there anyway. He always sits under a tamarind tree, a big tree with thick foliation that would protect him from a downpour. He might be able to pick up a few coins and buy enough rice to keep his little family from starving.

In addition to learning about the plight of so many Indian people, an American reader might learn a better appreciation of our relatively luxurious standard of living. Yet we have to admire these people for their fortitude. Most of them have lived like this from day to day for thousands of years. We share R. K. Narayan's sympathy for his people.