President Reagan yesterday sent to Congress a tuition tax-credit bill that would cost $1.5 billion a year by 1987. It contains anti-discrimination provisions that civil rights groups are attacking already.

The bill would allow parents to take a tax credit of up to 50 percent of each child's private school tuition, for a maximum of $100 in 1983, $300 in 1984 and $500, the maximum credit, in 1985 and thereafter.

The maximum would be phased out for families with incomes of more than $50,000 a year, and those with incomes of more than $75,000 a year would be ineligible. The credit would not apply to college students.

Gary L. Jones, undersecretary of education-designate, told reporters that the administration's cost estimates are based on the assumption that the tax credit would not increase enrollment from the estimated 4.5 million to 5 million private school students in the nation.

Sen. Robert J. Dole (R-Kan.) is expected to introduce the bill in the Senate today, Jones said, with Reps. Willis D. Gradison Jr. (R-Ohio) and Mario Biaggi (D-N.Y.) sponsoring it in the House. He said the administration will push for passage this year.

Support for such a measure in Congress has been lukewarm since Reagan announced the outline of the bill April 15 to Roman Catholic educators in Chicago. Many members saw it as a gesture to fulfill a campaign promise and boost the president's support among Catholic voters.

Even supporters like Dole have questioned the wisdom of pushing the bill at the same time Congress is wrestling with $100 billion deficits. A Dole aide said yesterday that it is unlikely that the tuition tax credit will be part of this year's tax bill.

Administration officials acknowledged that they delayed introducing the bill to try to work out an anti-discrimination clause acceptable both to civil rights groups and conservative church schools who have complained about Internal Revenue Service harassment.

The administration is still smarting from the outcry that followed the announcement in January that it no longer supported the IRS authority to bar exemptions to schools that discriminate.

The explanation accompanying the bill describes a three-pronged enforcement mechanism to ensure that racist schools don't benefit. Under the provisions, a tax credit could not be used unless a school met the IRS rules for being tax-exempt and filed an annual statement with the secretary of the treasury swearing it didn't discriminate.

In addition, the bill would allow a person who claims he has been discriminated against to file a complaint with the attorney general, who, in turn, could file a suit against the school. If the court found the school discriminatory, and all appeals were upheld, tax credits at that school could be disallowed for three years.

In the past, complaints were investigated by the IRS. But church schools complained about harassment, and Reagan promised to rein in the agency.

Norman Chachkin, of the Lawyers' Committee for Civil Rights Under Law, and Elaine Jones of the NAACP Legal Defense and Education Fund Inc., said yesterday that they told administration officials at a meeting last month that the enforcement provisions are not adequate because they would shift the burden of proof from the suspect schools to individual complainants.

"It's words without substance, a ruse," Jones said.

"We don't think this is any kind of advance at all," Chachkin said.