Sport first found its way onto/on to the Community agenda in 1984.
I think it should be "onto," but I'm not sure.
'onto' is correct.
You don't have to split this up unless the prepositions mean something different independently.
You can see this in these sentences: The man walked onto the road. The man walked past the shop and on to the pub. (He walked on, to the pub. He didn't walk onto the pub). Let's move onto the lawn.
Let's move on to our English lesson. (Let's move on, to our English lesson).
But even here, "Let's move onto our English lesson" could also be correct if the move is conceived that way.
anupumh is partly correct is saying that 'onto' is used for a change of position or state; but it's also used in other cases. And it doesn't have to be physical.
Sport wasn't on the agenda. Now it is. Sport moved onto the agenda.