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The use of non-probability data sources for statistical purposes has become increasingly popular in recent years, also in official statistics. However, statistical inference based on non-probability samples is made more difficult by nature of them being biased and not representative of the target population. In this paper we propose quantile balancing inverse probability weighting estimator (QBIPW) for non-probability samples. We use the idea of Harms and Duchesne (2006) which allows to include quantile information in the estimation process so known totals and distribution for auxiliary variables are being reproduced. We discuss the estimation of the QBIPW probabilities and its variance. Our simulation study has demonstrated that the proposed estimators are robust against model mis-specification and, as a result, help to reduce bias and mean squared error. Finally, we applied the proposed methods to estimate the share of vacancies aimed at Ukrainian workers in Poland using an integrated set of administrative and survey data about job vacancies.