Govind Ram Kejriwal, a retired government servant, held the ceremony at a small temple he frequents near the Girnar Tower in Kaushambi township.
The senior Kejriwal said he wanted Arvind Kejriwal to join the 'havan' but the latter could not as he is unwell.
He said he wanted his son's health -- the chief minister has been coughing away for days -- should improve and he should also be able to fulfil the promises he has made to the people.
"I held the havan to thank god," he added.
He described Kejriwal becoming the chief minister as "people's victory". He added that his son, a former income tax official and an activist, had "strong will-power".
"They (AAP) have just started preparations for the Lok Sabha election. Many good leaders have come and met us."
Will Arvind Kejriwal become the prime minister one day?
"It is god's decision who becomes the PM," the father added.
Kejriwal senior had offered prayers at the same temple before his son's swearing in ceremony Saturday.