You can dissolve corticosterone in 100% ethanol up to 10mM. This can then be diluted using something like sesame oil. I recommend heating while dissolving in ethanol. At 10mM in ethanol, corticosterone will not precipitate out of solution and can be stored for at least one month at -20C.
Don't dilute corticosterone dissolved in ethanol or dmso with saline. If you are using saline, I would recommend the HBC complex but again note the manufacturer's instructions. 3mg/kg for a rat is a pretty common "high" dose. The volume you inject depends on the concentration of your stock. For example, if you saturated your ethanol (10mM) and dilute to 5% of stock (1/20) your final concentration is .5mM. 3mg/kg for a 300g (.3kg) rat is .3kg*3mg/kg = .9 mg / rat. 0.5mM (0.0005M) is equivalently 0.0005*346.46g/L (the molecular weight of corticosterone, equivalently, 346.46mg/mL) = 0.17mg/ml and .9mg/.17mg/ml is 5.2ml. This is a really large injection volume. I would consider either using DMSO which has a solubility of 100mM, using Corticosterone HBC complex (which is soluble) or increase the concentration of your ethanol stock in the working solution. While some do dilute with saline or PBS, please note the attached product sheet which specifies max solubility of .5mg/ml for a 1:1 ethanol:PBS.