c. 1200, recenen, rekenen, "enumerate, count up; name one by one; relate, recount; make calculations," from Old English gerecenian "to explain, relate, recount; arrange in order," from Proto-Germanic *(ga)rakinaz "ready, straightforward" (source also of Old Frisian rekenia, Middle Dutch and Dutch rekenen, Old High German rehhanon, German rechnen, Gothic rahnjan "to count, reckon"), from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line," thus "to lead, rule."
The intransitive sense of "make a computation, cast up an account" is from c. 1300. From 1550s as "take into account." In I reckon the sense is "hold as a supposition or opinion, regard, consider as being," and the expression, used parenthetically, dates from c. 1600 and formerly was in literary use (Richardson, Swift, Jowett, etc.), but came to be associated with U.S. Southern dialect and thereafter was regarded by Anglophiles as provincial or vulgar. Related: Reckoned; reckoning.
For I reckon that the sufferings of this present time are not worthy to be compared with the glory which shall be revealed in us. [Romans viii.18]