This paper presents a characterization of L-band ionospheric scintillation observed at a single site in the polar region, and an analysis of GPS-based point positioning error caused by carrier phase data degradation during scintillation. The scintillation measurements of L1CA, L2C, and L5 signals have been made from Fairbanks, Alaska, using a Septentrio PolaRxS Pro scintillation receiver. The measurements include signal intensity and carrier phase sampled at 50 Hz, as well as S-4 and sigma(phi) indices at 1-minute cadence. The rate of TEC index (ROTI) measurements at 5-minute cadence have also been derived from the nominal GPS dual-frequency phase data collected by this receiver. In addition, measurements of standard deviation of code-carrier divergence (CCD-STD) fluctuations, which are affected by phase scintillation, are also provided by the receiver. Our analysis of observed amplitude and phase scintillation data during the auroral electrojet activity driven by space weather disturbances shows three types of scintillations: continuous, intermittent, and spike (primarily fade). Analysis of 50-Hz phase scintillation data and their 1-minute statistics (sigma(phi)) show that phase scintillation follows relation Delta phi(i)/Delta phi(j) = f(j)/f(i) or sigma(phi)i/sigma(phi)j = f(j)/f(i) between different radio frequencies, where phi(i). TEC/f(i) is the ionospheric-induced carrier phase advance at radio frequency f(i). The 1-minute statistics of amplitude scintillation (S-4) tend to follow roughly the relation too, but the high-rate signal intensity data show some decorrelation between different signals. It is also found that measurements of CCD-STD show a similar linear relation but at a higher slope than f(j)/f(i). Experiments of precise point positioning have also been conducted using the nominal dual-frequency (L1 and L2) pseudorange and carrier phase data and the GNSS Inferred Positioning System and Orbit Analysis Simulation Software (GIPSY-OASIS, briefly GIPSY). Forward-only Kinematic positioning approaches are applied to both quiet and disturbed conditions in order to compare positioning performances. It is shown that the positioning error can increase significantly which is caused by phase data degradation due to scintillation.