"Did you ever think...?" as used in the lyrics is correct. It implies that it might be a surprise that they are now so close; perhaps it had never occurred to the person that they would someday be close. So, this is a rare case where rock music lyrics don't use bad grammar. ;)
The difference with "have" is that "did" implies one moment in time, whereas "have" could include a range of time or multiple instances. If you use "have", first of all you need to say "Have you ever THOUGHT" (not "think"), and the meaning is not the same. You could say "Have you ever thought we could be as close as brothers?", but that means it hasn't happened yet, and is referring to future potential.
One common form of usage for "have" in a question is "Have you ever done/thought/been to/eaten/etc. ______ before?"