The closest Old English term for "linguistics" or "philology" is stæfcræft, literally "letter-skill", a calque of Greek γραμματικὴ τέχνη (grammatikē technē) "art of letters", based on γράμμα (gramma), "letter", which itself derives from γράφειν (graphein) "to write", originally meaning "to scratch" (Old English wrītan "to write" also originally meant "to scratch", cp. German reißen "to tear").
Ælfric of Eynsham (ca. 955-1010), in his translation/adaption of the Latin grammar Exceptiones de Prisciano into English, renders Latin grammatica "grammar" (< γραμματικὴ) as stæfcræft:
GRAMMA on grecisc is LITTERA on leden and on englisc stæf, and GRAMMATICA is stæfcræft.
"Gramma in Greek is littera in Latin and stæf ("letter") in English, and grammatica ("grammar") is stæfcræft."
In the preface to this Old English grammar of Latin, Ælfric says:
Ic ælfric wolde þas lytlan boc awendan to engliscum gereorde of ðam stæfcræfte, þe is gehaten GRAMMATICA, ... forðan ðe stæfcræft is seo cæg, ðe ðæra boca andgit unlicð; and ic þohte, þæt ðeos boc mihte fremian iungum cildum to anginne þæs cræftes, oððæt hi to maran andgyte becumon.
"I, Ælfric, wished to translate this little book on stæfcræft--which is called grammatica--into the English language ... because stæfcræft is the key, which unlocks the understanding of books; and I thought that this book might help young children in the beginning of the art, until they arrive at greater understanding."
Zupitza's edition of Ælfric's grammar and glossary is available on Google books.
High quality scans of St. John's College (Oxford) MS. 154 of Ælfric's text are available here.
For more on Ælfric's grammar, see Vivien Law's article on Ælfric's "Excerptiones de arte grammatica anglice".