1640s, American English, from birch (n.) + bark (n.1). Old English had beorcrind.
Entries linking to birch-bark
birch n.
"hardy, slender northern forest tree noted for its white bark," Old English berc, beorc (also the name of the rune for "b"), from Proto-Germanic *berkjon (source also of Old Saxon birka, Old Norse börk, Danish birk, Swedish and Icelandic björk (which is also a girl's given name), Middle Dutch berke, Dutch berk, Old High German birihha, German Birke).
This is from PIE *bhergo (source also of Ossetian barz, Old Church Slavonic breza, Russian bereza, Lithuanian beržas, Sanskrit bhurjah, all names of birch-like trees, Latin fraxinus "mountain ash"), from root *bhereg- "to shine; bright, white," in reference to the bark. Birch beer is by 1827, American English.
bark n.1
"tree skin, hard covering of plants," c. 1300, from a Scandinavian source akin to Old Norse börkr "bark," from Proto-Germanic *barkuz, which probably is related to birch and Low German borke. The native word was rind.