Amigny-Rouy is located some 30 km south of Saint Quentin and 25 km west by north-west of Laon. The commune is accessed by road D7 from Sinceny in the west passing through the heart of the commune and continuing east to Saint-Gobain. The D53 road comes from Condren in the north-west passing through the village and continuing south to Barisis. There is also a network of country roads throughout the commune. Most of the commune is farmland however there is a large forested area in the south forming part of an extensive forested area outside the commune. There are no other hamlets or villages in the commune.
The Oise river forms the northern and north-western border of the commune and the Ruisseau de Servais with numerous tributaries passes from east to west through the northern portion of the commune into the Oise. The Ru de Greve flows through the south of the commune. There are also a number of small lakes in the commune.
In 2009, the commune had 728 inhabitants. The evolution of the number of inhabitants is known through the population censuses conducted in the town since 1793. From the 21st century, a census of municipalities with fewer than 10,000 inhabitants is held every five years, unlike larger towns that have a sample survey every year.[Note 1][Note 2]
Gédéon Poizot, Lieutenant French Forces of the Interior (FFI), (born 26 June 1907 Amigny-Rouy - died 10 August 1944, at the edge of the Busigny woods), alias "Poulain-Germain," hero and martyr of the Resistance (Maquis Mazinghem), killed on 10 August 1944 by the Vichy Milice.
^At the beginning of the 21st century, the methods of identification have been modified by law No. 2002-276 of 27 February 2002 , the so-called "law of local democracy" and in particular Title V "census operations" which allow, after a transitional period running from 2004 to 2008, the annual publication of the legal population of the different French administrative districts. For municipalities with a population greater than 10,000 inhabitants, a sample survey is conducted annually, the entire territory of these municipalities is taken into account at the end of the period of five years. The first "legal population" after 1999 under this new law came into force in 1 January 2009 and was based on the census of 2006.
^In the census table and the graph, by convention in Wikipedia, and to allow a fair comparison between five yearly censuses, the principle has been retained for subsequent legal populations since 1999 displayed in the census table and the graph that shows populations for the years 2006, 2011, 2016, etc., as well as the latest legal population published by INSEE