There has recently been an increase in scholarship on the Holocaust in Romania so this is a great question. The Holocaust in Romania differed significantly based on geographic location. The borders of Romania were very fluid during the Second World War and a significant amount of territory changed hands. First Bessarabia and northern Bukovina were ceded to the USSR in late June 1940. In late August of 1940 northern Transylvania was ceded to Hungary and then in September Dubruja was ceded to Bulgaria. The ceding of this territory counted for about 30% of the prior Romanian territory. Then in 1941 Romania acquired the area of Transnistria between the Dniester and Bug rivers. The experience of the Holocaust differed between each of these locations and between these areas and the area that remained Romania.
In the Fall of 1940 the Romanian fascist leader General Ion Antonescu and the Iron Guard took control of the Romanian government and formed an alliance with Nazi Germany and the Axis powers. Though Romania had already had significant antisemitism and antisemitic laws the conditions grew worse under Antonescu. Romania had a history of violent antisemitism, with the infamous Kishinev pogrom having taken place only a few decades before. On January 21 of 1941 the Iron Guard rose up against Antonescu and during the three day civil war known as the Legionnaires' Rebellion, the Iron Guard along with a variety of civilians enacted a pogrom in Bucharest against the Jewish population, 125 Jews were killed in particularly gruesome ways which I will refrain from describing but which were so brutal that many of the methods used seem as though they belong in Silence of the Lambs rather than to the realm of history.
By the end of January Antonescu reinstated control with the help of the Germans and there was a lull in the slaughter until June. In June 1941 Romania participated in Operation Barbarossa, the invasion of the Soviet Union which would see the beginning of the more organized killing of Jews. During June the Romanian authorities, assisted by civilians enacted another pogrom, this time in Iasi. At least 4000 Jews were murdered in Iasi, on June 29 alone, most having been suffocated in sealed rail cars. As many as 15,000 were murdered throughout the 9 day pogrom, most were killed by Romanians, many by civilians, though the pogrom was supported by the Germans.
During the summer of 1941 Romania re-annexed Bessarabia and northern Bukovina and with the help of the German Einsatzgruppe D and local collaborators killed over 100,000 Bessarabian and Bukovinian Jews in mass shootings. In some places such as Kishinev they established ghettos and forced labor camps which would be liquidated by the end of 1941. During this same period, survivors of these massacres, as well as other Romanian Jews were deported to Transnistria (the region between the Dniester and Bug rivers which I mentioned before) where they were kept in ghettos and camps and where at least 120,000 of them were murdered, along with tens of thousands of local Jews.
In the areas of Transylvania ceded to Hungary the Jews survived until 1944 when the Germans occupied Hungary. About 165,000 Jews lived in this area, including author of "Night" Elie Wiesel. By May of 1944, just weeks before the Allies stormed the beaches of Normandy, the Jews of northern Transylvania were herded into ghettos. About 30,000 Jewish men would be kept in Hungary for slave labor, the rest were deported to Auschwitz, where most of them were murdered.

My focus is on the murder of Jews during the Holocaust, so this is not my field of expertise, but approximately 11,000 Romanian Roma/Sinti were also murdered in similar manners to Romania's Jewish population.
Because of territorial shifts it is difficult to determine exactly how many Romanian Jews were murdered in the Holocaust. In the territory of Romania today as well as in the area known as Transnistria during the war between 280-380,000 Jews were murdered according to the 2004 Wiesel Commission. Approximately another 135,000 were murdered in Transylvania when it was part of Hungary. Fewer than 5000 Jews live in Romania today.

Further Reading

"The History of the Holocaust in Romania" Jean Ancel
"Prelude to Mass Murder. The Pogrom in Iasi, Romania, June 29, 1941 and Thereafter"
by Jean Ancel
"The State, Antisemitism, and Collaboration in the Holocaust: The Borderlands of Romania and the Soviet Union" by Diana Dumitru
https://www.yadvashem.org/holocaust/about/final-solution-beginning/romania.html
https://encyclopedia.ushmm.org/content/en/article/romania
https://www.haaretz.com/jewish/.premium-1941-a-3-day-pogrom-starts-in-romania-1.5393169
https://www.ushmm.org/research/publications/academic-publications/full-list-of-academic-publications/the-iasi-pogrom
https://www.yadvashem.org/education/educational-materials/lesson-plans/iasi-pogrom.html
https://www.yadvashem.org/odot_pdf/Microsoft%20Word%20-%206327.pdf
https://www.yadvashem.org/odot_pdf/Microsoft%20Word%20-%205884.pdf
http://www.inshr-ew.ro/ro/files/Raport%20Final/Final_Report.pdf