Marin Dragnea was born on 1 January 1956 in Slobozia Moară, Romania.[1][3] He started playing football at the junior squads of Progresul București under coach Nicolae Gorgorin, starting to play at senior level in 1972 when the club was in Divizia B, being given his debut by coach Eugen Iordache and later working with Viorel Mateianu.[1][3] He was transferred to Dinamo București where he stayed one year without playing as he suffered a cruciate ligament injury while he was a player at Progresul which recurred when he played for them in a friendly.[1][3] In the following season he was loaned at FC Constanța where on 29 August 1976 he made his Divizia A debut in a 0–0 with his former team, Progresul.[1][3]
After one season, Dragnea left FC Constanța in order to return at Dinamo where he won three consecutive Divizia A titles from 1982 until 1984, at the first he contributed under the guidance of coach Valentin Stănescu with seven goals scored in 23 matches, in the second he played 30 games and netted seven once again and in the third he made 29 appearances and scored a personal record of 15 goals, at both working with coach Nicolae Dumitru.[1][3][4] He also won three Cupa României with The Red Dogs, in the first one he did not play in the final with FC Baia Mare, at the second, coach Dumitru used him the whole match in the 2–1 over rivalsSteaua București and at the one from 1986, under the guidance of coach Mircea Lucescu he played all the minutes in the 1–0 victory with Steaua who had recently just won the European Cup.[1][3][5] In November 1984, he would score the victory goal in a 2–1 over Steaua in a derby from the league.[6] Dragnea made some notable performances with Dinamo in European competitions as helping it eliminate Inter Milan in the 1981–82 UEFA Cup and appearing in eight matches in which he scored one goal against Kuusysi Lahti in the 1983–84 European Cup season, as the club eliminated title holders Hamburg in the campaign, reaching the semi-finals where the campaign ended in front of Liverpool.[1][3][7]
After nine and a half seasons spent at Dinamo, in the middle of the 1986–87 Divizia A season he was transferred at Flacăra Moreni where in three seasons and a half he made 109 Divizia A appearances in which he scored 21 goals and appeared in both legs of the 4–1 loss on aggregate in the first round of the 1989–90 UEFA Cup against FC Porto.[1][3][8] He ended his career by playing one season for Rapid București, making his last Divizia A appearance on 16 June 1991 in a 1–0 loss in front of Petrolul Ploiești, having a total of 405 matches with 85 goals scored in the competition, also he gained a total of 28 appearances in which he scored three goals in European competitions.[1][3]
Marin Dragnea coached teams from the Romanian lower leagues, his most notable period being at Unirea Urziceni when with players brought by him, he promoted the team from Divizia C to Divizia B in 2003.[11] After leading Unirea one more season and a half, he was replaced by Constantin Stănici, but half of year later when his former Dinamo teammate Costel Orac came as head coach, Dragnea worked as his assistant and together they managed to promote the team to Divizia A.[11] He also worked at Poiana Câmpina, ACS Berceni, Juventus Bascov and at junior level.[3][12][13]