Pronunciation of “tour”

John Wells, in his interesting and very readable paper Whatever happened to Received Pronunciation? makes the following observations about what is known as the CURE vowel, the diphthong /ʊə/, which a small number of speakers in the UK use for the word tour:

Decline and disappearance of /ʊə/. Words formerly containing the diphthong /ʊə/ have come increasingly to be pronounced with /ɔː/ instead. Thus your is no longer /jʊə/ but /jɔː/. Poor, sure, moor, cure, tourist are often /pɔː, ʃɔː, mɔː, kjɔː, ˈtɔːrɪst/. My survey figures for poor showed that when we group all ages together /pɔː/ was preferred over the traditional /pʊə/ by a margin of 57% to 43% of the respondents; but when we look at different age-groups separately /pɔː/ was preferred by only 27% of the oldest respondents (born before 1923) as against a massive 81% of the youngest (born since 1962). Words such as jury, rural seem generally to be resistant to this change, and do not rhyme with story, choral. Rather, they seem now typically to be pronounced with a monophthong of the [ʊː] type, perhaps to be interpreted as a variant of /uː/.

We can see there that the old CURE vowel, /ʊə/, has become virtually obsolete in the UK, certainly amongst RP speakers and has been replaced by /ɔ:/. The dictionaries seem to be a bit reticent about recognising this or giving /ɔ:/ as the predominant pronunciation. The Original Poster, however, specifically asks about /tɔ˞/ for the word tour, with an r-coloured vowel This is a rhoticised version of the modern RP one, and it would be surprising if there weren't some rhotic speakers in the UK who used it.