For free? Utopia! Impossible.
Explanation: imagine such a thing were possible. How many people would try to contact the psychologist? It would be such a mess... just like getting an autograph from a celebrity.
There was a chat (in my native language) where they claimed there were psychologists available for free... I joined at once, but it didn't take me long to find out no one in the chat room had ever even seen them... LOL.
In a forum (in my native language) I have seen a couple of psychotherapists and counselors though... you know, some of them join communities to advertise their activities while trying to help a little for free. They might answer in some threads they choose every once in a while, and that's it.
I expect the situation on the English part of the internet to be the same, so I'm not even looking for anything like that anymore. I know there are services like "Samaritans" or something, where there are people who will listen to you if you are suicidal or have problems... but they are not psychologists.
You can contact some psychologists online, some seem to do online therapy, or are willing to talk online anyway, but they'll charge something... not for free.