Chester A. Crocker, President Reagan's choice to be assistant secretary of state for African affairs, left on a two-week trip to a dozen African countries last night without benefit of being confirmed in that job by the Senate.

Crocker's problem, and he is not the only senior official in the State Department who suffers from it, is that while he is the president's choice for the job, he is not the choice of Sen. Jesse A. Helms (R-N.C.).

Helms has held up a number of State Department nominations, including Crocker's, prompting a complaint from Sen. Alan Cranston (D-Calif.) yesterday during hearings on Crocker's nomination.

Cranston said he could not recall another administration that had to wait this long to get so many key officials confirmed. "It is not the administration's fault," he said. "The fault lies right here in the Senate."

Helms replied that he was sorry if his questioning of administration nominees "offends some senators."

"I would just advise that it will continue," he said.

At yesterday's hearings, Helms questioned Crocker closely on his attitude toward the presence of Cuban troops in Angola and his selection of key aides in the bureau of African affairs. Helms was particularly critical of Crocker's decision to retain Lannon Walker as his chief deputy in the bureau, suggesting that Walker believes the Cubans are there only to prevent a potential invasion of Angola by South Africa.

Crocker was warmly praised by other members of the committee, but there was no committee vote on his nomination. Even before yesterday's hearing began, Helms, who has questioned whether a number of President Reagan's nominees are sufficiently conservative, had won agreement to continue the hearing on April 27, following Crocker's return from Africa.

When Sen. Nancy Kassebaum (R-Kan.) told Crocker that although he was going to Africa unconfirmed "but with our good will and our support," Helms added with a smile:

"And I wish you well, too. Have a nice trip."