Boss Dave Penney, keen to strengthen his squad, made his move after watching the youngster figure for Rovers in a pre-season friendly against Accrington Stanley.
Blackman began his career with Macclesfield before following former Silkmen boss Paul Ince to Ewood Park.
Swindon will be encouraged by their 1-0 win, their first of the season, against Southampton, courtesy of Sean Morrison's header.
Oldham are hopeful Danny Whitaker will be available after a virus ruled him out of Tuesday's 1-0 defeat at Millwall.
Key opponent: Billy Paynter - experienced and dangerous forward
Prediction: Oldham 2 Swindon 1 - Home advantage should swing it for Latics
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