No, Satan is not a fallen angel. God tells us in the Bible that angels do not sin, so they cannot “fall”: angels only do what God wants them to do:
“Bless the Lord, O you his angels, you mighty ones who do his word, obeying the voice of his word!” (Psalm 103:20)
Angels obey what God says. Likewise, Heb. 1:14 says that all angels are ‘ministering spirits sent out to serve for the sake of those who are to inherit salvation’.
“Are they not all ministering spirits, sent out to provide service for the sake of those who will inherit salvation?” (Hebrews 1:14)
Note the word all. Not all angels except the ones who are not.
These two passages are clear. Angels are God’s workers and they only do what God asks them to do. This goes against the idea – an idea with not a single Bible verse to support it – that Satan was once an angel who sinned against God.
See also:
How did Satan fall to earth? (Luke 10:18)
Where did the name “Lucifer” come from?
Who was the “cherub in Eden” (Ezekiel 28:13-14)?