We study the evolution of twist and magnetic helicity in the coronal fields of active regions as they emerge. We use multi-day sequences of SoHO MDI magnetograms to characterize the region's emergence. We quantify the overall twist in the coronal field, α, by matching a linear force-free field to bright coronal structures in EUV images. At the beginning of emergence all regions studied have α 0. As the active region grows, α increases and reaches a plateau within approximately one day of emergence. The inferred helicity transport rate is larger than differential rotation could produce. Following Longcope & Welsch (2000) we develop a model for the injection of helicity into the corona by the emergence of a twisted flux tube. This model predicts a ramp-up period of approximately one day. The observed time-history α(t) is fit by this model assuming reasonable values for the sub-photospheric Alfvén speed. The implication is that helicity is carried by twisted flux tubes rising from the convection zone, and transported across the photosphere by spinning of the poles driven by magnetic torque.