Archer spent time in the youth team at Chasetown, before scoring on his debut for the reserves in November 2011, and making his Northern Premier League Premier Division debut in a 1–0 defeat to Marine on 3 March 2012. After eight appearances for the "Scholars" in the 2011–12 relegation season, Archer moved on to Coleshill Town, making his debut for the "Colemen" in a 2–0 victory over Alvechurch at Pack Meadow on 6 August 2013. He made a total of seven Midland Football Alliance appearances and one FA Cup qualification appearance, scoring his first goal in senior football with a penalty in a 4–0 win at Continental Star on 14 August. He went on to play for Cradley Town, Tipton Town and Tividale. He joined Redditch United on 4 June 2015. However he struggled to get games for the "Reds" as Luke Shearer and Daniel Dubidat were preferred up front by manager Liam McDonald, and he was loaned out to Boldmere St. Michaels. Archer moved on to Bedworth United in September 2015. Despite him scoring 16 goals from 34 league games, the "Greenbacks" were relegated out of the Southern League Premier Division at the end of the 2015–16 season. The Warwickshire-based club were placed in the Northern Premier League Division One South for the 2016–17 season. He joined Stourbridge on 6 November 2016. He worked at a bank during his time at Stourbridge. Stourbridge reached the Northern Premier League Premier Division play-offs and he scored in their play-off semi-final victory over Workington at the War Memorial Athletic Ground, though they were beaten by Spennymoor Town in the final. During his 11 months with the "Glassboys" he scored 22 goals in 51 appearances, and spent a week on trial at Walsall in summer 2017. On 24 October 2017, he turned professional after being signed to a two-year contract by National League side Chester. "Blues" manager Marcus Bignot said that he believed Archer could play in the Football League.
Bury
On 12 July 2018, Archer signed a two-year contract with League Two side Bury after being bought for an undisclosed fee. "Shakers" manager Ryan Lowe said that Archer was "a wanted man" and praised sporting director Les Dykes and chairman Stewart Day for completing the deal. On 31 August, he joined National League side Maidenhead United on a two-month loan at York Road. He played eight games for Alan Devonshire's "Magpies". On 9 November, he joined National League North side Southport on a two-month loan deal at Haig Avenue. "Sandgrounders" manager Liam Watson went on to extend Archer's loan until the end of the 2018–19 season. He won the Liverpool Senior Cup with Southport, after they beat Prescot Cables on penalties after drawing the final 0–0. He was not paid for the last five months of his time at Gigg Lane and had to rely on 50% of his wages being paid by the Professional Footballers' Association.
Port Vale
Bury were expelled from the English Football League on 30 August 2019, and Archer signed a one-year deal with League Two club Port Vale the following day. He was signed by manager John Askey to provide competition for strikers Tom Pope, Richie Bennett and Mark Cullen. He made his debut for the "Valiants" on 3 September, coming on as a 60th-minute substitute for Tom Pope in an EFL Trophy tie with Shrewsbury Town at Vale Park; he went on to score the winning goal on 75 minutes as Vale came from behind to win 2–1. He dislocated his shoulder injury four days later, but rejected a shoulder operation in favour of physiotherapy as he wanted to avoid a lengthy spell on the sidelines recovering from surgery. On 17 January 2020, he joined National League play-off chasing side Stockport County on a one-month loan. Manager Jim Gannon said that he signed Archer to help arrest the "Hatters" dip in form, saying "I believe the new signings will add extra dimensions to us, add physical presence and the quality that has gone missing". However he was limited to just three appearances due to injury. He was released by Port Vale at the end of the 2019–20 season.
Style of play
Speaking in June 2015, Redditch United manager Liam McDonald said that Archer is "strong and fast and knows where goal is."
