Various point defects in silicon are studied theoretically from the point view of positron annihilation spectroscopy. Properties of a positron trapped at a single vacancy, divacancy, vacancy-oxygen complexes $({\mathrm{VO}}_{n}),$ and divacancy-oxygen complex are investigated. In addition to the positron lifetime and positron binding energy to defects, we also calculate the momentum distribution of annihilation photons (MDAP) for high momenta, which has been recently shown to be a useful quantity for defect identification in semiconductors. The influence of atomic relaxations around defects on positron properties is also examined. Mutual differences among the high momentum parts of the MDAP for various defects studied are mostly considerable, which can be used for the experimental defect determination.