To qualify for this timeline, the orbital rocket had to be designed and engineered in its entirely in the country. The rocket must also have successfully delivered a payload to orbit.
Note that all orbital launches on this timeline originated from government programs.
1957
October 4
Soviet Union
Russia took over the Soviet space program after the Soviet Union’s dissolution in 1991
1958
February 1
United States
Currently has orbital launch capability including human spaceflight
1965
November 26
France
Currently has orbital launch capabilities as a member of ESA
1970
February 11
Japan
Currently has orbital launch capability
1970
April 24
China
Currently has orbital launch capability including human spaceflight
1971
October 28
United Kingdom
Currently has orbital launch capabilities as a member of ESA
1979
December 24
ESA (an intergovernmental organization)
Currently has orbital launch capability which is available to all members. Ongoing discussion regarding the need to develop human spaceflight capability.
1980
July 18
India
Currently has orbital launch capability and is actively working on developing human spaceflight capability.
1998
September 19
Israel
Currently has orbital launch capability
1991
September 28
Ukraine
Currently has orbital launch capability
1992
January 21
Russia
Currently has orbital launch capability including human spaceflight
2009
February 2
Iran
Currently has orbital launch capability
2012
December 12
North Korea
Currently has orbital launch capability
2022
June 21
South Korea
Currently has orbital launch capability
Source: Wikipedia