You can select the texture sample in the material editor and change the mip setting to either “Mip Bias” or “Mip Level”. ‘Mip bias’ lets you bias the existing mip values and ‘mip level’ lets you set it explicitly, such as with the “compute mip level” function. Note that when using ‘compute mip level’ you will get bilinear and not anisotropic mip mapping.
Looking at your above image though, I feel like there may be something else going on. What resolution is your texture? Have you tried different settings for the mip mapping in the texture settings (ie various levels of sharpen).
Is your texture square?