Air carrier crew continues down Taxiway K rather than turning onto Taxiway T12 to hold short of Runway 32L at ORD.

Narrative

ORD ground gave us taxi clearance; 'taxi Runway 32L full length via Kilo.' Runway 32L requires a turn onto Taxiway T12 to get to Runway 32L full length. I miss read the airport diagram thinking Taxiway T12 was to an intersection of Runway 32L and continued on Taxiway K. The First Officer was reading the before takeoff checklist. At the turn for Taxiway T12 the First Officer asked if we were to turn at Taxiway T12 and that was when I stated that that was an intersection after rechecking the chart and not the full length and he agreed. ATC advised us that we missed Runway 32L and gave us further taxi instructions to Runway 32L. We had briefed the taxi route prior to block out; but on taxiing out I miss read the chart and the First Officer didn't catch the error. We followed SOPs; no unnecessary conversation while taxiing. There were no signs on Taxiway K directing us to turn on to Taxiway T12 to get to Runway 32L and I feel this was a factor. ATC clearance could also have been more specific; ie 'taxi Runway 32L full length via Taxiway Kilo T12.