Is "to anagram" an established verb?

The general form is 'A is an anagram of B'

Anagram - noun

1 - a word, phrase, or sentence formed from another by rearranging its letters: “Angel” is an anagram of “glean.”.

www.dictionary.com

Thus in your example:

To his amusement, Jason realized that 'Madam Curie' was an anagram of 'Radium Came'

Anagram is not a verb — although any word can be verbed, it weirds English.

The verb form is anagrammatise [ODO].

However, consider rearrange:

To his amusement, Jason realized that the words Madam Curie could be rearranged to Radium came.

anagram is indeed a verb, and anagrammatize its alternative form. Ngram

anagram (anagrammed; anagrammimg)

transitive verb

1: anagrammatize

2: to rearrange (the letters of a text) in order to discover a hidden message M-W

To his amusement, Jason realized that the words "Madam Curie" anagrammed into "Radium Came"

"L.A. Woman" anagrams into "AWOL Man" Google Books