The party says the move would support almost 50,000 jobs in Scotland and boost the proportion of homes available to poorer families.
The Scottish Government has set out plans to build at least 50,000 affordable homes by 2021.
Ministers say the target represents a 67 per cent increase in affordable housing supply, with 35,000 of the 50,000 to be available for social rent.
Figures show 4,629 new build social rent homes were completed in 2017/18.
However Labour says the rate of completion should be increased to reduce social housing waiting lists.
The party said its goal to build 12,000 homes each year is a “long term target” which would be reviewed on the basis of need.
It estimates the annual cost at £1.7 billion in the first year, shared by government, councils, registered social landlords and other partners.
Mr Leonard said: “A home should be a basic and fundamental human right.
“That’s why a Scottish Labour government would ensure access to a safe, secure, habitable, home by aiming to build at least 12,000 homes for social rent every year.
“Our society is deeply divided, with the richest 1 per cent in Scotland owning more personal wealth than the whole of the poorest 50 per cent.
“This is no time to tinker around the edges, not when so many people in Scotland are currently waiting for public housing.
“Scotland’s housing crisis is a key reason for deepening poverty in Scotland. People can’t access social homes so find themselves in the under regulated private rented sector. We have to address it urgently.
“When Labour was last in power we built 61,000 homes for social rent in Scotland - we desperately need that kind of ambition again.”