Technically it's free - but realistically, it's not. Here's why:
The test, in and for itself, is free - at least this is what scrumalliance claims (however if you fail the test more than two times than any subsequent tests towards the same certification will cost you $25 each).
However, the test is not really free, here's why:
- You will need to take a course about Scrum with scrumalliance (scrumalliance do not mention that you have to take the Scrum course with them, but I assume that this is the rule)
- That course is a two day course that costs money
- You take the Scrum test at the end of the course
There are probably other Scrum certifications out there, but the one offered by scrumalliance is the most recognized.