Although President Reagan's grace period for young men who failed to register for the draft comes to an end today, one of every eight required to fill out a card has failed to do so.

The Selective Service System said more than 927,000 had not signed up by the middle of last week. The Justice Department has said it could take two to eight weeks to begin to notify non-registrants that they have violated the law.

Non-registration is a felony punishable by up to five years in prison and a $10,000 fine. It also is a felony not to notify Selective Service of a change of address. So far, 1 million of the almost 7 million young men who have registered for the draft have told the Selective Service they have moved.

This is a little more than half the people in the 18-to-21 age bracket who might be expected to move since draft registration resumed in 1980.

"We've had moving notices from 15 percent of our registrant population," Joan Lamb, Selective Service public affairs officer said recently. "The Census Bureau tells us we should expect 25 percent to move."

Lamb said registration of the more than 8 million American men born in 1960 to early 1964 will be recorded on Selective Service computer tapes by the first week of April. If everyone required to register has done so, there will be about 8,054,000 names on the tapes.

Men whose names are not on the tapes will be sent warnings, first by the Selective Service and then by the Justice Department, which has said it will prosecute those who continue to refuse to register.

"There certainly will be hundreds," Attorney General William French Smith said earlier this month when asked how many prosecutions Justice plans. "How many more is difficult to say." The administration intends to enforce the draft registration law, he said, "within our existing resources."

Draft-resister organizations say they have been told that Justice was preparing cases in December against 40 young men who publicly acknowledged they had not registered and that the department had sent letters of warning to 183 who had not registered.

This was before President Reagan extended the grace period that ends tonight.

"The cases Justice was getting ready for the grand jury were the easy ones, those who were refusing to register for religious reasons," said Barry Lynn, president of the anti-registration group called Draft Action. "Religious protests of the draft don't carry much weight in the courts."

The Selective Service has said that those who refuse to register are not being fair to the 7,126,496 who have registered.

Since a draft would take place by lottery, the Selective Service says the draft would be fair only if 98 percent of those required to register did so. Right now, less than 90 percent appear to have registered.