It depends — "as" is lowercase in AP Style and Chicago Style but capitalized in NYT Style.
"As" is a two-letter word that functions as a preposition, conjunction, or adverb depending on context. In most of these roles it is lowercase in AP Style, Chicago Style, MLA Style, and AMA Style, but capitalized in NYT Style.
Chicago Style explicitly lists "as" among the words to be lowercased in titles, reflecting both its prepositional use and its conjunction use. At two letters, it falls well within the four-letter lowercase threshold for prepositions.
When "as" functions as an adverb of degree — as in "twice as fast" — it carries more independent meaning and some style guides treat it as a capitalized adverb. In practice, this distinction rarely arises in title contexts.
NYT Style capitalizes "as" along with other prepositions and conjunctions as part of its convention of heavier capitalization. Billboard Style capitalizes every word including "as" without exception.
"As" is one of the shorter and more versatile words in English. When it functions as a preposition — as in "working as a writer" — or as a conjunction — as in "as long as you know" — AP Style and Chicago Style lowercase it in the middle of a title.