The Alexandria City Council gave its public housing authority permission last night to issue $20 million in tax-exempt bonds for construction of an apartment complex in the city's West End.

The developer, Thomas Herr of Midlands Investments Inc., will be required to set aside 20 percent of the proposed 206 units to be constructed at N. Beauregard and N. Armistead streets for low-income residents at reduced rates. Low-income renters would pay up to 30 percent of their income for renting the one-bedroom and efficiency units reserved for them.

Council approval of the bonds to be issued by the Alexandria Redevelopment and Housing Authority represents an effort to get more rental property in Alexandria, where officials perceive a shortage.

Expected rents on two-bedroom units would be over $1,000 a month, according to the developer. Some council members were skeptical that many renters would pay that much.

Rental income from the 80 percent of residents who do not fall in the low-income category will provide most of the funds to manage the complex and service the debt on the bonds.

Despite these reservations, council members said they thought there was no other way to encourage more rental housing for low-income families, since the discontinuation of some federal rent subsidies. "It's the only way to go," said Mayor Charles E. Beatley.

The apartment complex is set to be completed in 1986. The units set aside for low-income residents will be provided for 10 years from the date on which the complex reaches 50 percent occupancy.

In other action the council approved allocation of $5,000 from a contingency reserve fund to support emergency shelters for the homeless through January 1985. Additional funds may be made available pending a public hearing on the homeless issue set for Dec. 15.