If the apostrophe in "ar't" is simply an error by the author, it is not the only one on this page. For example, I note three occurrences of the word "did[']st"—two without an apostrophe (didst) and one with an apostrophe (did'st). The presence or absence of the apostrophe in the case of didst is arguably acceptable either way—since didst could be read as a contracted form of "didest [thou]"—presumably the ancestral form from which didst sprang. Nevertheless, the lack of consistency in the writer's handling of didst on this page raises the possibility that he viewed apostrophes as something closer to optional ornaments than to necessary elements.
Less immediately explicable than the inconsistent treatment of didst and did'st is the word hope't in line 12 of the poem:
Or didst thou hasten headlong to prevent
A fruitlesse hope't for needfull parliament?
In modern U.S. English, an editor would probably render that second line as follows:
A fruitless, hoped-for, needful Parliament?
—so it isn't as though the apostrophe in hope't signals the loss of, say, an s from hopest. If anything, hopet is a letter too long to begin with: after all, writers generally see no reason to add an e (or an apostrophe) before the t in burnt or learnt or spoilt or spilt. (Admittedly, none of those root verbs ends with an e.) The case would be different if the word in the line had been hop'd—since that spelling clearly involves the loss of an e.
However, in a comment beneath this answer, Peter Shor points out that the spelling "hope't" helps the writer avoid a misreading of hopt or hop't as short forms of hopped, as well as to signal to readers that the word is not to be read as having two syllables (as they might if he had simply rendered the word as "hopet." As for the writer's wish to avoid "hop'd" (aside from the fact that it, too, might, be misread as a short form of "hopped"), he seems scrupulous in distinguishing between past-tense verbs and verblike adjectives ending in a "d" sound ("return'd," "distempered," "gorg'd," "wrong'd" "bespotted," "tortur'd," compos'd," "oppressed") from those ending in a "t" sound ("hope't," "vex't").
(Speaking of orthographic anomalies, in line 17, the writer renders "there's" as "their's":
But their's a reason worse, then this, they say
—an unusual spelling to choose for a common word, although far more forgivable in 1630 than it would be today. Interchangeable use of then for than, on the other hand, seems to have been quite common in the seventeenth and eighteenth centuries.)
Returning to the line that the poster is primarily interested in:
And ar't return'd againe wth all thy faults
one might argue that "ar't" is doing duty for two words—"art thou." However, "art" alone could have accomplished the same thing, since "art" implies "art thou," just as "dost" (as used in this poem) implies "dost thou." It seems extremely unlikely that the writer chose the spelling "ar't" because he wanted to create a contraction of the form "ar[t]'t[hou]." I can't think of any similar use of an apostrophe to create a contraction that begins at the front of one word and ends at the front of a second word.
I consider it far more likely that the writer simply stuck the apostrophe in "ar't" on an unconsidered or ill-considered whim, without any sense that it was marking the loss of one or more letters from one or two contracted words. If you had access to more than this single page of the manuscript, you could check to see whether the writer consistently uses "ar't" for "art thou," or whether this is simply a variant form that slipped in (like "did'st" in line 9).
My guess is that the writer usually rendered the word as "art" with no apostrophe, but that on this occasion his pen or his wandering thoughts led him to a different orthographic choice. I strongly doubt, in any case, that his use of the form "ar't" was intended to adhere to some established rule of punctuation that prevailed in 1630—because I don't think that any such convention with regard to "ar[']t" existed.
Neevertheless, it is quite possible that the writer views the apostrophe as having a far wider range of uses than the modern big three of elision/contraction, possession, and pluralization. The example of "hope't" in this page indicates that the writer may use the apostrophe to indicate a pronunciation shortened from two syllables to one—and perhaps he also considers it useful for other obscure or idiosyncratic purposes, such as to distinguish "art" used in one basic sense of the word from another.