The figure smashed the previous record of 37,774 for a game between Crystal Palace and Millwall at Selhurst Park in 1961 in the old English fourth division.
The Ibrox crowd was larger than the combined attendance for last weekend's five Scottish Premier League matches of 40,383.
Rangers, the 54-times Scottish champions and one half of the Glasgow "Old Firm" that has dominated Scottish football for decades, were playing their first home league match outside the top flight as they begin to recover from a financial crisis.
The club went into administration in February before a takeover in June, and were demoted from the SPL to the third division - the bottom of the country's footballing pyramid - after a meeting of Scottish Football League clubs last month.
Ranges opened their campaign last weekend with a 2-2 draw against Peterhead in front of 4,500 fans at Balmoor stadium on the north-east coast of Scotland.
