Before I lived in the UK, I thought 'reckon' was a Southern expression.
"Reckon" is complicated, the Oxford English Dictionary divides it into literally dozens of distinct meanings. The sense of "I reckon" meaning "I believe, I expect or I think" seems to be archaic English that had largely faded away in formal usage but has survived in colloquial usage, in dialect, in places like the US South.
The OED has these early published instances;
1567 J. JEWEL Def. Apol. Churche Eng. II. ix. 200 But for further answeare, I recken, M. Hardinge cannot be ignorant, that [etc.].
1748 S. RICHARDSON Clarissa V. xlvi. 326, I shall have a good deal of trouble, I reckon,..to be decent on the expected occasion.