Is it possible to pass Facebook Graph API access token through request header?

Yes it is possible

Authorization: Bearer AccessTokenHere

e.g.

curl --header "Authorization: Bearer CAAC...ZD" https://graph.facebook.com/me

_{This answer previously recommended using “OAuth” instead of “Bearer” as the token type. Both will work, but “Bearer” is the type that shows up in the standard. Also, on completing Facebook’s OAuth flow, the token_type in their response is bearer. So all in all “Bearer” makes more sense.}