For an APA paper, the title I have chosen is Art Through the Ages. Should the word "through" be in caps?

Yes....

Thank you. I wasn't sure because "Word" kept signifying that it should be in lower caps.

http://www.grammarbook.com/punctuation/capital.asp

Below is the general rule I use.

Rule 8 Always capitalize the first and last words of titles of publications regardless of their parts of speech. Capitalize other words within titles, including the short verb forms Is, Are, and Be.

Exception Do not capitalize little words within titles such as a, an, the, but, as, if, and, or, nor, or prepositions, regardless of their length.
Examples The Day of the Jackal
What Color Is Your Parachute?
A Tale of Two Cities

Thank you. I will copy this for a reference. Appreciate you shedding some light on this simple but important rule.

In APA style, the general rule is to capitalize the first word and any proper nouns in the title of your paper. However, it is not necessary to capitalize prepositions of four letters or fewer, such as "through." Therefore, in your chosen title, "Art Through the Ages," you should capitalize only the first word "Art" and the proper noun "Ages." The word "through" should be in lowercase.