The verb 'call' has many meanings. As @Zachiel has said, it can mean 'cry out', and most other answers seem to agree:
Oxford has the second definition for this meaning of 'call':
2 [with object] Cry out (a word or words)
‘he heard an insistent voice calling his name’
‘Meredith was already calling out a greeting’
But I disagree with this interpretation of 'call' in the given context. Instead, I'd say that the 'call' here means the seventh definition of Oxford:
7 [with object and complement] (of an umpire or other official in a game) pronounce (a ball, stroke, etc.) to be the thing specified.
‘the linesman called the ball wide’
Let me first show the whole transcript of the video that includes "we call BS":
(1) Politicians who sit in their gilded House and Senate seats funded by the NRA telling us nothing could have been done to prevent this, we call BS.
(2) They say tougher guns laws do not decrease gun violence. We call BS.
(3) They say a good guy with a gun stops a bad guy with a gun. We call BS.
(4) They say guns are just tools like knives and are as dangerous as cars. We call BS.
(5) They say no laws could have prevented the hundreds of senseless tragedies that have occurred. We call BS.
(6) That us kids don't know what we're talking about, that we're too young to understand how the government works. We call BS.
As seen above, "we call BS" in this context is not intended to be a standalone phrase, but is intended to be construed along with the boldfaced phrase or clause that acts like an object of the verb 'call', and 'BS' acts like a predicative complement of the object.
Now, the object is fronted because it's way too long (even a clause) to come between the verb 'call' and the predicative complement 'BS'.
If the verb 'call' simply means 'cry out', then the relationship between the verb and what comes before 'we call BS' becomes unclear. Therefore, I think it's better to think of the verb as defined in the seventh definition above.