The poll was triggered when sitting Conservative MP Stephen Phillips quit last week over "irreconcilable policy differences" with the government.
Ms Evans said she wanted to be an MP in order to put pressure on the government over Brexit.
The by-election is expected to take place before the end of the year.
On Thursday, three High Court judges ruled the government cannot officially notify the EU of its intention to leave, thus beginning formal talks, without Parliament's support.
Lincolnshire voters were among the most Eurosceptic in the UK, with more than 75% of voters in Boston voting to leave.
Parts of the county have in recent years seen an influx of EU workers drawn to the area's agricultural industry.
Ms Evans said: "The people of Lincolnshire voted to leave the European Union, and it looks as though the establishment is trying to renege on that.
"We've had the High Court decision which is a clear attempt to frustrate the will of the British people, and is completely unacceptable."
She accused the political classes of continuing to "kowtow to the European Union", adding that if elected she would force PM Theresa May "to get us out".
UKIP will announce its new leader on 28 November, with Paul Nuttall and John Rees-Evans the rival candidates to Ms Evans.
In last year's election in Sleaford and North Hykeham, Mr Phillips won a majority of 24,115, with 56% of the vote. Labour finished second, closely followed by UKIP.
Others to have expressed interest in standing in the constituency include Conservative councillor Richard Davies, Joseph Hyatt for the Independents, and UKIP's Victoria Ayling and Robin Hunter-Clarke.
UKIP leadership race contender Suzanne Evans says she will put herself forward to represent the party in the Sleaford and North Hykeham by-election.