Is “are” a borrowed word?

The verb be has a complex history, being a hodgepodge porridge of three entirely different original verbs, with some forms of one lost to suppletion by forms of another. Another familiar verb with suppletive forms is go and went, where the past of wend replaced that of go.

Back to be.

The singular am had two competing plurals, one of which earon, aron was cognate to Old Norse eru, and the other was sind as in German. The German-looking form was replaced by more regular-looking inflections of be itself like ben and even best and beth. The are forms like aron, aren, arn, are survived only in the north, but gradually spread south. For a time at the birth of what we today call Modern English, both competing forms were found.

All this and much more is explained in the OED’s etymology entry for be (verb), an extremely small excerpt of which I enclose below.

An irregular and defective verb, the full conjugation of which in modern Eng. is effected by a union of the surviving inflexions of three originally distinct and independent verbs, viz.

1. the original Aryan substantive verb with stem es-, Skr. as-, ’s-, Gr. ’εσ-, L. es-, ’s-, OTeut. *es-, ’s-;
2. the verb with stem wes-, Skr. vas- to remain, OTeut. wes-, Gothic wis-an to remain, stay, continue to be, OS., OE., OHG. wesan, OFris. wes-a, ONor. ver-a;
3. the stem beu- Skr. bhū-, bhaw-, Gr. φυ-, L. fu-, OTeut. *beu-, beo-, OE. béo-n to become, come to be.

Of the stem es-, OE. (like the oldest extant Teutonic) possessed only the present tenses, Indicative and Subjunctive (orig. Optative), all the other parts being supplied from the stem wes-, pa. t. was, which, though still a distinct and complete vb. in Gothic, was in OE. only supplemental to es-, the two constituting the substantive verb am-was. Béon, be, was still in OE. a distinct verb (having all the present, but no past tenses) meaning to ‘become, come to be’, and thus often serving as a future tense to am-was. By the beginning of the 13th c., the Infinitive and Participle, Imperative, and pres. Subjunctive of am-was, became successively obsolete, the corresponding parts of be taking their place, so that the whole verb am-was-be is now commonly called from its infinitive, ‘the verb to be,’ although be is no part of the substantive verb originally, but only a later accretion replacing original parts now lost.

In OE. the present Indic. of am had two forms of the plural, (1) sind, sindon (= Goth. and Ger. sind, L. sunt, Skr. sánti) and earon, aron (= ONor. eru), the latter confined to the Anglian dialects, where it was used side by side with sind, -un. Of these, sind, -on ceased to be used before 1250, its place being taken in southern Eng. by the corresponding inflexions of be. We, ye, they beth, ben, be, were the standard forms in southern and midl. Eng. for centuries; and even in the sing., be, beest, beth began to encroach on am, art, is, and are now the regular forms in southern dialect speech. Meanwhile aron, aren, arn, are, survived in the north, and gradually spread south, till early in 16th c. are made its appearance in standard Eng., where it was regularly used by Tindale. Be continued in concurrent use till the end of the century (see Shakspere, and Bible of 1611), and still occurs as a poetic archaism, as well as in certain traditional expressions and familiar quotations of 16th c. origin, as ‘the powers that be.’ But the regular modern Eng. plural is are, which now tends to oust be even from the subjunctive. Southern and eastern dialect speech retains be both in singular and plural, as ‘I be a going,’ ‘we be ready.’

Perhaps you were thinking we borrowed are from Old Norse, but in fact, it was only a cognate. On the other hand, just possibly the Nordic invasions and settlements may perhaps have influenced the continued use of the are forms.