Sen. Robert Dole (R-Kan.) went to the steps of the Internal Revenue Service building here yesterday to call attention to the step-up in taxes American pay as a result of inflated incomes.

The occasion was a carefully staged press conference by Dole in front of the IRS to win public support for his bill to index personnel income tax rates and exemptions to the inflation rate.

Such indexing is not a new idea, but its political popularity seems to grow as increases in the national cost of living accelerate. With inflation now running strong, many incomes have been carried up sharply, too, only to be taxed more in the end.

Dole cited a recent study that showed 77 percent of America's taxpayers are paying higher taxes because of inflation -- $9 billion more in 1978, $11.5 billion more in 1979 and an expected $15.6 billion more in 1980.

"That's what we call 'bracket creep'," the senator declared, tagging the whole phenomenon "taxflation."

Dole said inflated tax payments amount to a "windfall profit" for government. "It has often been said that nobody benefits from inflation," said Dole, the ranking Republican on the Senate Finance Committee. "But that is obviously not true. The federal government benefits a great deal from inflation each and every year."

Past attempts at enacting an inflation index for taxes have met with little favor among Treasury officials who worry it would reduce federal budget-making flexibility.

Key congressional leaders also generally haven't supported tax indexing, preferring to retain the political advantages that come from legislating tax cuts during election years.

But Dole said such cuts are misleading. He argued instead for the automatic adjustments that indexing would bring. "It would take the politics out of" keeping taxes down, the senator declared, adding that it also "would bring about some discipline for Congress."

As for what the public favors, Dole referred to a Roper Organization poll last year in which 57 percent of those surveyed preferred indexing to the periodic tax cuts made to keep taxes in line with inflation. Thirty-two percent preferred the periodic cuts.

Dole said that six states -- Arizona, Colorado, California, Iowa, Minnesota and Wisconsin -- have adopted indexing. Rep. Willis Gradison (R-Ohio) has introduced legislation in the House similar to Dole's.

Dole claimed there is considerable bipartisan support for his bill, though he said he has yet to convince Sen. Russell Long (D-La.), chairman of the Finance Committee, to support it.

To illustrate the effect of taxflation, Dole referred to a typical family of four earning $15,000 this year. Assuming an inflation rate of 8 percent -- in fact, it is expected to be much higher this year -- Dole said the family will have to earn $1,200 more in 1980, or $16,200, just to stay even with inflation. But while their income increases by 8 percent, their income taxes actually increase by $258, or about 12.6 percent, Dole said.

The impact on a wealthier family is even greater,he said.