The year is 2117 C.E. and it seems that human and machines have coexisted amicably for many decades, these androids had filled almost every roles from judges to member of the parliament all except police officer. I was wondering if car can go driverless why not robot cops? What we have instead are cyborg, technology worn by people to supervise other people in the name of law and more specifically it is forbidden for a non-human to enforce law in the society! We have deployed terminators across borders and overseas to deal with the enemies which consist of mostly human beings during war time hence suggesting that robot laws are bendable!
It's beneath them.
Robots come in different classes from menial worker drones to sophisticated leaders and decision makers. The type of subtle on-the-spot decision making required to be a police officer is only found in the higher castes of robot and these types have more rewarding jobs to do.
They can't take the oath.
The oath of office requires something like "... to protect and serve all the citizens and to enforce the law ...". For an important declaration such as this, robots are not able to ignore the logical contradiction between enforcing the law and serving a citizen who happens to be a criminal.
The ancient law makes them ineligible
Based on centuries of legal precedent, a (human) suspect is only legally arrested if the arrest is made by a human. A robot may be able to physically stop a criminal but the arrest will not stand up in court without a human police officer on hand.
They're takin' our jerbs!
There is a strong (human) police union which is able to reserve police jobs for humans based on specious political arguments.
Separate but equal
Human crime is policed by humans and robot crime is policed by robots. It just happens that there is much less robot crime and it tends to be cyber crime that does not require a cop on the beat.
Law enforcement often relies on interpersonal communication and relationships. Law officers also need to make very sensitive decisions, including ones involving letting a petty criminal go in exchange for information.
Your androids might lack 'human' touch when it comes to the delicate business of keeping peace and order. For example, they may be following laws, rules, and regulations to a T. They might be unable to bend their views and behaviour, which would result in an inability to collect useful intelligence. Therefore, they simply will not be effective as a police force.
Another explanation would be prejudice against androids. Humans might believe that machines are lower than they are, incapable of understanding humans or making moral decisions.
It is also possible that criminals destroy androids way too often and the cost of having robocops is just too high.
And of course, it is much easier to hack a robot and turn it into a weapon than a breathing living human being. A precedent like this would be a perfect fit for your no-android-cops law.
Are you asking for plausible reasons as to why, despite the advances in technology you have described coming into being, robot cops are still expressly banned by law?
I would say that enforcing the law on the streets requires a human touch, but given that a robot can be programmed to effectively pass judgement in a court of law, that seems unlikely.
I would then suggest that perhaps the human police force happened to be the strongest labour union in force, and actively lobbied against being replaced by robots, so that they are the last predominantly human workforce left. However, this is again unlikely if so many other functions have already been replaced.
Lastly, perhaps this is due to social response - criminals have been found to respond differently to human and mechanical law enforcers. A trial batch of robot cops were tested, with the finding that criminals resorted to violence much earlier when confronted with machines, leading to greater collateral damage. Human cops were therefore more effective at reducing violence, and so remain an institution despite all technological progress. (Again, this may be unlikely since in such a mech-proliferate world as yours, humans probably react to machines in more or less the same way they do to other human beings.)
Protectionism and privacy
An early law says that each human being must own a robot before any organization can. The human being receives the wages that the robot earns. Also, any extra robots cannot start doing jobs until the individual-owned robots are fully employed.
The police unions negotiate an extra protection for their members. All actual law enforcement activities like arrests and interrogations must be conducted by humans. Robots can do paperwork, fetch coffee, record crime scenes, and disarm bombs or weapon-using opponents.
In an agreement supported both by police unions and by privacy advocates, robots are restricted from collecting evidence before a crime. Otherwise, police could just have a robot follow and surveil each human being. The evidence from robots before a crime is committed isn't usable as evidence as an extension of precedents like United States v. Antoine Jones and Torrey Dale Grady v. North Carolina. So any proactive policing, like a foot or car patrol, must be done by a human.
The basic idea is that mechanical surveillance must be limited by human capabilities to avoid violation of the fourth amendment. So while robots can assist, only things witnessed by a human may be used as evidence.
This is somewhat US-centric but allows for a path for a society. You just need some of the same legal precedents as actually happened in the United States (US) to be extended in this way.