I found https://tzscan.io/network?state=all via this Reddit post where the current amount is around 6 800 nodes.
There are two directions this amount maybe is not the absolute one, though:
A) post says it does not count private nodes nor self bakers
B) without state = all the amount was 79, which is significantly lower, denoting most probably ones currently active.
So, hard to say. Maybe Tzscan.io API would reveal which number to believe.
This is sitation under Network in the API:
The Network is the list of Nodes running the Tezos Server Application. From any Node, including the Nodes used by Tz-Scan, only a partial part of the full network is visible, mostly through the Node to which the Node could successfully connect.