Linking for what is sure to be a hard drive ahead, President Carter and Sen. Edward Kennedy (D-Mass.) have agreed to introduce jointly next week a bill to deregulate the trucking industry.

In a background briefing yesterday at the White House, Carter and Kennedy aides told reporters they had resolved what had been minor differences between them on the issue. Carter is expected to make a statement on the final version of the proposal after he returns from the Vienna summit.

Both the president and the senator in recent weeks have been quietly circulating in Congress first drafts of a deregulation bill. The aim of the measures was the same - to foster a more competitive trucking industry subject to marketplace forces rather than regulation by the Interstate Commerce Commission.

It was disclosed yesterday that Kennedy, who has been teasing and taunting the president for months, phoned Carter last Friday to suggest the two of them team up and present a joint proposal. Aides for both men spent the week working out a compromise on the few details on which they had disagreed.

The chief difference had involved the fate of the ICC. Kennedy wanted to write in a definite date for the termination of the commission's authority over the trucking industry. Carter was reluctant to go as far.

The final version calls for a study in 1983, prepared by the Justice and Transportation Departments, to determine the eventual role of the ICC.

By that time, though, if the proposed bill passes, the ICC will already have been substantially weakened, with many of its powers over trucking either cancelled or transferred to other agencies.

In broad term, the proposal would knock down many entry barriers for new trucking companies. It would also allow carriers more freedom in setting prices within a so-called "zone of reasonableness."

Further, the bill would remove restrictions limiting types of commodities that trucking companies can transport and the routes they must follow, and it would exempt from ICC regulation altogether all agricultural and horticultural commodities, as well as farm implements, fertilizers and chemicals.

One section that will be in the final proposal that was in neither Carter's nor Kennedy's first draft provides for stricter industry safety standards. In addition to setting higher fines for violations, the bill would provide job protection for workers who report such violations to the government.

The bill is expected to run into powerful opposition from the trucking industry. One Carter aide yesterday said the fight for trucking deregulation would be much tougher than the one for airline deregulation had been in part "because consumers don't travel around in trucks."

But proponents of deregulation contend that a more competitive trucking industry would also lead to substantial price reductions for consumers.

Despite promises by Carter early in his term to deregulate trucking, the White House has been slow to act here, preferring to move first to lift restraints on the airlines and railroads.In part, this has been because trucking regulation involves a web of rules and procedures considerably more complex and extensive. Another reason, too, is that the ICC has been less supportive of a complete overhaul than was Civil Aeronautics Board under Alfred Kahn.

In related news yesterday, nine former ICC commissioners continued federal regulation of the nation's surface transportation industry. In a joint statement, they criticized administration efforts to deregulate the railroad, trucking and intercity bus business.