The first solar radio polarization observations at 3 mm (86 GHz) and 13 mm (22 GHz) were made at Aalto University Metsähovi Radio Observatory in Finland in spring 2019. This was the first time that 3 mm (86 GHz) and 13 mm (1.3 cm) solar polarization observations were made with the same radio telescope. In this paper we describe the observing system and data analysis, and present the first results. We also compare our data with polarization observations made with the Nobeyama Radioheliograph and find that the results are consistent. Additionally, we determine the quiet Sun level brightness temperature at 3 mm (86 GHz) using the New Moon for refererence, and obtain a mean value of 6310 K.