To me it is false. It appears the people spreading such claims have a fundamental misunderstanding of genetics. The vaccine contains a fragment of the virus's genetic material - or RNA. "Injecting RNA into a person doesn't do anything to the DNA of a human cell," The vaccine "does not alter the DNA sequence of a human body. It only presents the body with the instructions to build immunity".
That's not true! If we really wanted to control humanity, there are several ways. For example, they could force us to wear a bracelet with a chip like prisoners. Also, all our information and movements are recorded in our phones and laptops. So why this "imaginary" chip in the vaccine?