Yes, angels can sin.  Satan is a fallen angel, and he sinned.  Also, the Bible tells us that angels have sinned in 2 Peter.

 2 Pet. 2:4, “For if God did not spare angels when they sinned, but cast them into hell and committed them to pits of darkness, reserved for judgment.”

Obviously, angels possess enough free will to be able to make choices, but not all angels have sinned.  1 Tim. 5:21 tells us there are elect angels.  They are the ones who were kept by God from sin. Nevertheless, if even some angels sin, then we know that angels can sin.

Before the creation of the world, there was a rebellion in heaven, and many of the angels fell with Satan.  Many theologians believe one-third of the angels fell as may be referenced in Rev. 12:4, “And his tail swept away a third of the stars of heaven, and threw them to the earth. And the dragon stood before the woman who was about to give birth, so that when she gave birth he might devour her child.” Jesus even tells us that the eternal fires and punishments of hell were prepared for “the devil and his angels,” (Matt. 25:41). This makes little sense unless angels can sin.

Thus, the answer is very easy.  Yes, angels can sin.  Here are some more verses on the topic:

• Job 4:18, “He puts no trust even in His servants; and against His angels He charges error.”
• Luke 10:18, “And He said to them, ‘I was watching Satan fall from heaven like lightning.”
• Jude 6, “And the angels which kept not their first estate, but left their own habitation, he hath reserved in everlasting chains under darkness unto the judgment of the great day.”
• Rev. 12:9, “And the great dragon was cast out, that old serpent, called the Devil, and Satan, which deceives the whole world: he was cast out into the earth, and his angels were cast out with him.”