Can testosterone affect the kidneys? The answer is’yes’, since testosterone affects everything in a male. In fact, testosterone can affect the kidneys in several counterintuitive ways that most men on HRT (testosterone therapy) may not be aware of. One is generally positive and the other generally negative. And, unfortunately, by negative I mean that in some cases testosterone replacement therapy could actually aggravate or harm the kidneys in certain sensitive men.
In addition, it is one reason many men probably do not want to go too high in their testosterone level if they are on HRT. Consider this discussion below:
1. Erythropoieten. This kidney hormone is responsible for triggering your red blood cell production in the bone marrow and testosterone ramps both erythropoieten and red blood cell production upwards significantly. In fact, low testosterone men are quite often anemic because of it and men who go on HRT need to monitored to make sure their RBC count, hemocrit or hemoglobin does not go too high. This can have some serious consequences, which I discuss in my link on Ways to Lower Hemoglobin.
Does simply raising erythropoieten cause any issues with the kidneys? Well, not directly. However, there is evidence that in some men with hypertension, testosterone therapy can further raise their blood pressure. And any increase in blood pressure can potentially, over time, injure the delicate vessels in the kidneys. When these blood vessels get injured, the kidneys struggle to do their job and eliminate wastes, etc. This can lead to an increase in fluids. Are you sensing a vicious cycle here? Yes, as the fluids increase, blood pressure increases and so on. This can be a big problem for diabetics and men with advanced kidney disease.
NOTE: One interesting fact about erythropoitin is that it is also called EPO, a name that may be more familiar to some of you. Yes, that should bring the name Lance Armstrong to mind. Lance Armstrong confessed to using EPO as a performance enhancing drug strictly for the purpose of raising his red blood cell counts for racing purposes. Basically, he was doing a different and very dangerous kind of steroid. Giving EPO to these racers leaves them vulnerable to dieing in their sleep from the “sludging” of the blood that occurs. It does turn them into superhumans however.
2. Contraindicated for Advanced Kidney Disease. There are some sources that recommend that testosterone therapy not be given to men with kidney disease, even if they are hypogonadal.  The reason for this is that testosterone could potentially aggravate or inflame the kidneys for these men according to their thinking. Healthy men can hold this process in check without chronic injury, but these experts would not take chances in those who are vulnerable.
The primary reason is that testosterone appears to “promote apoptotic damage in human renal tubular cells.”  Several animal studies showed this effect and then researchers repeated the test in vitro.  Apoptosis basically refers to the “programmed cell death” that many kinds of cells have latent within them. Testosterone basically accelerates this condition according to the above anyway.
Further study work has identified other key ways that testosterone may be questionable for those with kideny issues:
a) ” increase tubular sodium”
b) “water reabsorption”
c) “activate various vasoconstrictor systems in the kidney, such as the renin-angiotensin system and endothelin.”
d) ” increase oxidative stress.” 
Furthermore, I don’t believe we have had a single legitimate complaint of a kideny issue on the Peak Testosterone Forum related to testosterone therapy. We had one man who thought he had an issue actually:
“Can the shot cause kidney issues?? Ever since I got the shot on Thursday in my right hip. My left kidney lower back has had a constant pain almost like I got a kidney stone.. 1st shot I had issues with my tongue feeling like it was to big for my mouth. Now this.. Any ideas??” 
However, it tunred out that he had a small kidney stone!
Bottom line: get screened before and after for kidney function and discuss with your physician. How do you check kidney function? Well, this is a big subject of course, but here are some or all of the standard tests: GFR (Gromurular Filtration Rate) and creatinine clearance.
3) Kidney International, 2004, 65:1252 1261; “Testosterone promotes apoptotic damage in human renal tubular cells”
<4) AJP – Renal Physiol, Nov 1 2005, 289(5):F941-F948, “Testosterone supplementation in aging men and women: possible impact on cardiovascular-renal disease”5) Journal of Biological Chemistry, 279:52282-52292, “Testosterone Is Responsible for Enhanced Susceptibility of Males to Ischemic Renal Injury*”6) https://peaktestosterone.com/forum/index.php?topic=1607.msg15492#msg15492
7) The Journal of Urology, Jul 2006, 176(1):15 21, “Sex Differences and the Role of Sex Steroids in Renal Injury”