I have seen other similar questions and someone mentioned radar measurements made in the 1960's. Who did that and when and where? I am not interested in ancient measurements. Only the currently accepted measurement, And when it was made.
There never has been a direct measurement of the distance between the Earth and the Sun. The best we can do is measure the distance between the Earth and the other planets, and from that infer the distance between the Earth and the Sun.
Today's estimates aren't based on radar pings from Venus. That is so last millennium! Early 1960s, to be precise. That said, estimates of the astronomical unit made possible by those 1960s radar measurements of the distance between the Earth and Venus were much more precise than were prior estimates based on parallax, reducing the uncertainty in the astronomical unit from 16000 km to less than 1000 km.
In the 50+ years since that time, space agencies have sent spacecraft to all of the other seven planets in the solar system (other than the Earth, of course), plus Pluto, plus some asteroids, plus some orbiting the Sun. The telemetry from those spacecraft, augmented by very long baseline interferometry (VLBI), have made those measurements from the 1960s look rather imprecise. The latest work was in 2009 by Pitjeva and Standish, who stated the uncertainty in the astronomical unit as being 3 meters. No work has been done on measuring the AU since then because the astronomical unit is now a defined quantity, exactly 149597870700 meters (the value stated by Pitjeva and Standish).