The 23-year-old made his debut this season with Manor Racing, who have made big progress despite being the smallest team on the starting grid, but the deal requires a budget contribution.
Indonesian media has put the amount needed at 15 million euros (12 million pounds), with state-owned oil and gas company Pertamina paying five million and the Ministry of Tourism also assisting.
The latest initiative, backed by the Indonesian government and telecoms companies, aims to raise money by encouraging fans to show support by texting RIO to the number 7788. Haryanto races with the number 88 on his car.
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"Basically it's the sports minister's idea to generate funding," Haryanto told Reuters at the Russian Grand Prix on Thursday. "They want to get as much as they can to get the budget for Formula One.
"You send a text message to the number and then its about 5,000 rupiah (0.259 pounds) per message if you are willing to support me to have some extra funding.
"It's been going already for one week and I don't know what amount we have got so far. It's going quite well and we'll see what's the result," added the driver.
Haryanto has 467,000 followers on Twitter alone, more than many established F1 racers, while Indonesia has a population of around 250 million.
Communications Minister Rudiantara told CNN Indonesia that supporters should make their texting "like taking medicine, three times a day".
Manor, with Mercedes engines and new team management, have been much more competitive this season after failing to score a point in 2015 when they raced as Marussia.
"This year we can fight with the Sauber and Renault and every race we are still making progress," said Haryanto, who was second in a GP2 race in Sochi last year.
"It's good to be back to the tracks that I know," added the driver, who plans to base himself in Spain during the European season.
"Here I have good memories, being on the podium last year in GP2. It's just already a step ahead to know the track a bit more."
(Reporting by Alan Baldwin, editing by Toby Davis)
