An unarmed Langley Park man was arrested by uniformed Secret Service officers yesterday after he scaled a White House fence and ran to near the bottom of a stairway that leads to the West Wing, where President Reagan's office is located, authorities said.

The president was in his residential quarters, several hundred feet away, when the incident occurred, Secret Service spokesman Rich Adams said.

Mike Davis, 25, was arrested at 3:30 p.m. and told Secret Service officers that he was "astroplaning" or "attempting to catch the sun," officials said.

"He jumped the northwest gate, took off running and was arrested running from the gate," Adams said. The gate is part of an iron fence about eight feet high that surrounds the grounds enclosing the White House complex.

It is not unusual for intruders to scale the White House fence, but they are usually stopped after only a few feet.

Davis had gone about 100 feet, officials said.

Davis was turned over to District police for questioning. He has been charged with unlawful entry and was awaiting arraignment yesterday evening.