With a heavy security guard, Rosalynn Carter arrived here today to voice American support for Colombia's democratic government and to discuss the problem of international drug smuggling.

Leftist students have held sporadic demonstrations against the government of President Alfonso Lopez Michelsen, and three universities have been closed. Yesterday the U.S. consulate in Cali, about 200 miles southwest of here, was bombed. There was little damage and no one was hurt.

Military police were at the airport and teams of civilian police lined the motorcade route as Mrs. Carter went to the American-Colombian cultural center and then to the U.S. embassy.

There were no incidents today and no anti-American signs near the stops on Mrs. Carter's itinerary.

Colombia is a close ally of the United States and it is reported to have a good record in respecting the human rights of its citizens.

Narcotics is an important item on the agenda because thousands of tons of marijuana and cocaine are smuggled into the United States each year from Colombia. The $500 million that Colombian drug dealers receive each year, mostly from U.S. buyers, contributes to Colombia's 30 per cent annual inflation rate.

Mrs. Carter, who is scheduled to meet with Lopez Friday, is expected to discuss ways the the two nations can cooperate to slow the drug traffic. She is also expected to discuss the plight of about 70 Americans jailed in Colombia on drug charges.

Mrs. Carter, who is touring seven Latin American nations, flew here from Recife, Brazil. She apparently made no major breakthroughs in her discussions with Brazilian leaders, but U.S. officials said her visit was useful in getting a new dialogue started after six months of strained relations between the two countries.

The Journal do Brasil, a leading Brazilian newspaper said yesterday, "By spending the major part of her time on human rights, she has demonstrated once again that the United States has a new policy: If they cannot make other countries respect human rights, they make it clear that those who disregard these rights will not find an ally in Washington."

O Estado do Sao Paulo, another respected national paper, said that "the information gathered by Mrs. Carter may not sufficient to give her mission any really practical meaning. She may leave Brazil with a wrong impression caused by the friendly reception given to her by authorities."