No, Albania has never been part of Romania. They are two distinct sovereign nations in different subregions of Europe.
Both were part of the Ottoman sphere of influence at different times, and both experienced communist rule in the 20th century, but they have never shared a political union. Albania declared independence from the Ottoman Empire in 1912; Romania's modern statehood emerged from the principalities of Moldavia and Wallachia in the 19th century.
Confusion sometimes arises from the similar-sounding names or the fact that both are Eastern European countries that transitioned from communism in the 1990s. However, their histories, languages (Albanian is an isolate Indo-European branch; Romanian is Romance), and cultures are entirely separate.