The Rev. Jesse L. Jackson made appearances in Prince George's and Anne Arundel counties yesterday, mixing politics with his customary appeals for good citizenship.

In Prince George's, he spoke to 2,000 students at Largo High School. In what has become his standard routine, he urged them to work hard in school and swear off drugs. Hundreds of emotional students poured on to the school's football field, admitting that they had tried drugs or alcohol.

Political implications of Jackson's visit were perceived by Kettering businessman Bennie L. Thayer, who said this week that he is seriously considering a bid for the 5th District congressional seat now held by Rep. Steny Hoyer and hopes to have Jackson's help in such a campaign.

Thayer said before Jackson's visit, which he organized, that "we see it as a kick-off spur for the Rainbow Coalition in Prince George's County, as a start to roll into the 1986 agenda."

Thayer is the head of the Maryland Rainbow Coalition, which gave Jackson a victory in the 1984 Democratic presidential primary in Prince George's County.

Jackson also called on the students to assume their responsibility and express their patriotism by registering to vote. "Most students in the world do not have a right to vote," he said, challenging the students to graduate "with a diploma in one hand and a voter registration card in the other hand."

Later in the day in Annapolis, Jackson inspected a city housing complex and urged its residents to vote for Carl O. Snowden, an antidiscrimination consultant who is running for the City Council.

Jackson said he visited Robinwood, an apartment complex on the south side of the city, because that is where the city's poorest people live. He complained that the federal government is spending money on missiles and bombs, at the expense of health and housing.

He repeated his message of support for Snowden last night at the First Baptist Church in Annapolis, calling Snowden a "coworker in the struggle" on behalf of those locked out of the political system.

Snowden, a Democrat who has complained the city provides too little low-cost housing, is running against Republican Myron V. Wotring in the city's primarily black 5th Ward.