See our wiki page on [[Insurance & Actuarial]]. Yes, wou can be an actuary with an economics degree, as long as you have excellent maths skills, and can show evidence of this to your prospective employer.
You could join a [[big 4]] firm, or an insurance firm, or another firm from this [[list of insurance and actuarial firms]]. Don’t worry too much about not having an actuarial science degree.
Alternatives would be self-study on an actuarial course whilst working somewhere else, but really, you might as well joing a graduate actuarial training programme, where your employer would pay for/cover the costs of this course themselves.