Word to describe 100% success in an exam

To ace an exam is to complete it with high marks - typically referring to a 100% or higher (in the case of bonus marks). Per Oxford Dictionary, ace:

(North American) achieve high marks in (a test or exam): I aced my grammar test.

In Commonwealth English at least, the phrase "full marks" is commonly used to refer to the highest score that it is possible to get, i.e. 100%. If you find MacMillan's definition to be slightly ambiguous ("the highest score that a student can get" could be taken to mean "the highest score that a particular individual is capable of"), the Wiktionary entry is less so: "the maximum marks obtainable in an exam or test."

In a sentence, therefore, "I got full marks in the exam" would be used. Although this is not a verb or single word as your question states you would prefer, in my opinion the verbs given in the other suggested answers do not unambiguously indicate that the score was exactly 100%, as opposed to being a score that the speaker would personally consider more than expected / satisfactory. Someone struggling with a certain subject could subjectively consider a personal high score for exams in that subject to be very good and describe it as such ("nailed", "aced", etc.), without that score being anywhere near 100%.

Consider,

I nailed the exam.

nail (Slang):

To perform successfully or have noteworthy success in: nailed the dive; nailed the exam. The American Heritage® Dictionary

To accomplish (a task) completely and successfully. I really nailed that test. Your Dictionary

To execute or accomplish flawlessly: the gymnast nailed her routine. Webster's New World College Dictionary

I passed the exam with flying colors.

pass with flying colors: with complete or outstanding success: passed the exam with flying colors. (American Heritage® Dictionary)

EDIT:

One other possibility would be to say,

I got a full score on the exam. WordReference