Two separate questions are being asked here. First there is the confrontation between James and Paul at the Council of Jerusalem, in Acts 15, and then there is the separate question of the riots, followed by Paul’s arrest by the Roman authorities, in Acts 22-23.
It’s pretty clear what’s going on at the Council of Jerusalem (Acts 15). Paul’s Gentile flock in Antioch are chafing under an array of demands that mean, for them, that the Christian Church is still too Jewish, while James’ Jewish Christians in Jerusalem are pulling in the opposite direction: they’re not willing to allow Christian worship to drift too far away from Judaism.
In connection with the second episode, the riot and Paul’s subsequent arrest, the question is, Why didn’t James come to his rescue? But this would imply that James wielded some kind of influence over the citizens of Jerusalem as a whole, rather than within the narrower confines of the Christian community alone. But did he, in fact, enjoy such broad-based prestige? Would it have been within his powers either (a) to swing the opinion of the Sanhedrin to Paul’s side, or (b) to convince the Roman authorities to release him? I have always been given to understand that the answer to both questions is No.