Lets take a look at the text in question:
Romans 13:1 Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God. (2) Therefore whoever resists the authority resists the ordinance of God, and those who resist will bring judgment on themselves. (3) For rulers are not a terror to good works, but to evil. Do you want to be unafraid of the authority? Do what is good, and you will have praise from the same. (4) For he is God’s minister to you for good. But if you do evil, be afraid; for he does not bear the sword in vain; for he is God’s minister, an avenger to execute wrath on him who practices evil. (5) Therefore you must be subject, not only because of wrath but also for conscience’ sake. (6) For because of this you also pay taxes, for they are God’s ministers attending continually to this very thing. (7) Render therefore to all their due: taxes to whom taxes are due, customs to whom customs, fear to whom fear, honor to whom honor.
This passage discusses the Christian’s duty to submit to civil government. The teaching here is actually an expanded version of Christ’s words, "Render therefore to Caesar the things that are Caesar’s" (Matthew 22:21).
Everyone should submit to the "governing authorities" (human rulers). We must submit to them because God is the source of all authority and He has established existing rulers. This does not mean God chooses, appoints, or approves every individual leader (although no one can exercise power unless God allows it). Rather, God has established the general principle of human government.