From Longman Dictionary of Contemporary Englishsign on phrasal verb1 British EnglishPEW to state officially that you are unemployed by signing a form, so that you can get money from the government2 PMSIGN YOUR NAMEto sign a document to show that you agree to work for someone as He signed on as a soldier in the US army. with I’ll probably have to sign on with a nursing agency. → sign→ See Verb table
Examples from the Corpus
sign with• Most clients sign on with a handshake.• Warning Before signing on with an agency: 1.• One hundred and fifty communities and schools signed on with Global ReLeaf as tree planters.• His pal Stretch, for whom anything new is a potential high, decides to sign on with him.• When Romney lost to Richard Nixon, Fisher signed on with him.From Longman Business Dictionarysign on phrasal verb1[intransitive] British English to go to your local job centre and sign a form which states officially that you are unemployed, so that you can get money from the governmentChildcare Allowance is available only for married women whose children are over four years of age and who have been signing on for the previous six months.2[intransitive, transitive] sign somebody → on if you sign on, or sign someone on, you sign or persuade someone to sign a document agreeing to do something, for example accepting a job, studying on a course, or becoming involved in a business dealTwo more members of staff were signed on full-time. asJacobs signed on as a junior attorney with a Santa Rosa law firm. toThe corporation is deciding whether to sign on to a deal to build a new U.S. manufacturing plant to compete with the French.3[intransitive]COMPUTING to start using a computer system, the Internet, or to go to a websiteYou’ll need to type in your password to sign on to the network.The Internet has strange economics; individual users are charged for signing on, but can then surf the net for nothing. → compare log on under log1 → sign→ See Verb table 