Ben Cook, Justin Mankis, and Kevin Anchukaitis have an extremely helpful review paper in Current Climate Change Reports (ungated, thanks) sorting out what we do and don’t know about the impact of climate change on droughts.
The IPCC’s Fifth Assessment Report was cautious in its assessment of our knowledge of drought, reporting only “low confidence” in then-current assessments of the detection and attribution of a climate change impact on drought:
In the years since the AR5 was published, however, there have been steady advancements in our understanding of drought dynamics and the associated physical processes. These insights have been generated through further development of the paleoclimate record, new analyses of recent and historical drought events, and the widespread use and interrogation of climate models.
Focusing on Colorado River streamflow, Woodhouse et al.  compared this most recent drought period (2000–2012) against similar magnitude droughts in the 1950s (1950–1956) and 1960s (1959–1969). They found that while both the 1950s and 1960s droughts were linked to significant precipitation deficits, precipitation in the basin was near normal in the 2000s and this latest drought was likely driven by the much warmer temperatures. Udall et al.  subsequently concluded that historical warming of 0.9?C has reduced Colorado River flow by 2.7–9%, which would account for roughly one third of flow losses during the 2000–2014 drought in the basin. McCabe et al.  found similar effects of warming on streamflow in the Upper Colorado River Basin, attributing reductions in streamflow of 7% over the last three decades to increased evapotranspiration and snowmelt from warming in the spring and summer (April–September).
Our knowledge of climate change and drought has advanced considerably since the publication of the AR5. This expanded body of knowledge includes numerous studiesthat more confidently attribute recent droughts to climate change and paleoclimate analyses that highlight the unusual severity of recent droughts in the long-term context of the Common Era. These findings represent a marked shift from the much more conservative statements regarding drought and climate change in the AR5, which were appropriate for the time given the state of the science.