Anisotropy.java

import com.badlogic.gdx.Gdx;
import com.badlogic.gdx.graphics.GL20;
import com.badlogic.gdx.graphics.Texture;
import com.badlogic.gdx.utils.BufferUtils;

import java.nio.FloatBuffer;

public class Anisotropy {

    private static boolean anisotropySupported    = false;
    private static boolean checkComplete          = false;
    private static float   maxAnisotropySupported = 1.0f;

    /**
     * Applies the given anisotropic level to the texture. Returns the anisotropy value that was applied, based on
     * device's maximum capability. Note that this call binds the texture if the device supports anisotropy.
     *
     * @param texture    The texture to apply anisotropy to.
     * @param anisotropy The anisotropic level to apply. (Will be reduced if device capability is less.
     * @return The anisotropic level that was applied, or `1.0f` if anisotropy is not supported by the device.
     */
    public static float setTextureAnisotropy(Texture texture, float anisotropy) {
        if(!checkComplete)
            isSupported();
        if(anisotropySupported) {
            texture.bind();
            float valueApplied = Math.min(maxAnisotropySupported, anisotropy);
            Gdx.gl20.glTexParameterf(GL20.GL_TEXTURE_2D, GL20.GL_TEXTURE_MAX_ANISOTROPY_EXT, valueApplied);
            return valueApplied;
        } else {
            return 1f;
        }
    }

    /**
     * @return Whether the device supports anisotropic filtering.
     */
    public static boolean isSupported() {
        GL20 gl = Gdx.gl;
        if(gl != null) {
            if(Gdx.graphics.supportsExtension("GL_EXT_texture_filter_anisotropic")) {
                anisotropySupported = true;
                FloatBuffer buffer = BufferUtils.newFloatBuffer(16);
                buffer.position(0);
                buffer.limit(buffer.capacity());
                Gdx.gl20.glGetFloatv(GL20.GL_MAX_TEXTURE_MAX_ANISOTROPY_EXT, buffer);
                maxAnisotropySupported = buffer.get(0);
            }
            checkComplete = true;
        }
        return anisotropySupported;
    }

    /**
     * @return The max anisotropic filtering level supported by device, or 1 if it isn't supported.
     */
    public static float getMaxAnisotropySupported() {
        if(!checkComplete)
            isSupported();
        return maxAnisotropySupported;
    }
}

Usage:

Anisotropy.setTextureAnisotropy(texture, level);

level is usually power of two values from 1 to 16. For me 4 works great.