G­órecka em­barked on her mu­si­cal jour­ney very early, be­ing born into a fam­ily of mu­si­cians, with her mother, Jad­­wiga Górecka, a pi­anist and her fa­ther, Hen­ryk Mikołaj Górecki, a com­poser. This pro­vided her with the priv­i­lege of be­ing in con­tact with live mu­sic and em­i­nent artists from a young age. At the age of four, she be­gan pi­ano lessons un­der the guid­ance of the fa­mous Pro­fes­sor Wanda Chmie­low­ska and later con­tin­ued her stud­ies with Bożena Dymek and Marta Cz­erewko. 

She grad­u­ated with dis­tinc­tion from the Acad­emy of Mu­sic in Ka­tow­ice in 1991, study­ing un­der Pro­fes­sor An­drzej Jasiński, the teacher of Krys­t­ian Zimer­man. At her grad­u­a­tion con­cert, she per­formed Sergei Rach­mani­nof­f’s Pi­ano Con­­certo No. 3 in D mi­nor with the Sile­sian Phil­har­monic. In the same year, she be­gan a two-year course at the Hoch­schu­­le für Musik in Trossin­gen un­der the leg­endary Russ­ian pi­­a­nist and teacher, Pro­fes­sor Vik­tor Merz­ha­nov. She also great­ly ben­e­fited from mas­ter­classes with Pro­fes­sor Lee Kum Sing.

Górecka re­ceived schol­ar­ships from the Min­istry of Cul­ture and Art and the Deutscher Akademis­cher Aus­tau­sch­­di­enst. She is a prizewin­ner of sev­eral pres­ti­gious pi­ano com­pe­ti­tions, in­clud­ing the In­con­tro In­ter­nazionale Gio­vani Pi­a­nisti in Seni­gal­lia (1982), the Pol­ish Pi­ano Fes­ti­val in Słupsk (1991), and the In­ter­na­tional Brahms Com­pe­ti­tion in Ham­burg (1992).

While still study­ing, she en­gaged in an ac­tive con­cert ca­reer. Her de­but at Lon­don's Wig­more Hall in 1994 was hailed by crit­ics as a "pi­anis­tic tri­umph," launch­ing her in­ter­na­tional ca­reer. Górecka has since un­der­taken nu­mer­ous con­cert tours, in­clud­ing per­for­mances in Japan (in 1993 with Sin­fo­nia Varso­via and in 1996 with the Sile­sian Phil­har­monic), the UK (in 1996 with The Great Sym­phony Or­ches­tra of Pol­ish Ra­dio and Tele­vi­sion in Ka­tow­ice), and Spain (in 2002 with the Sile­sian Phil­har­monic).

She per­forms in some of the most pres­ti­gious con­cert halls in Poland and around the world, in­clud­ing the Ber­lin Phil­har­mo­nic, the Great Hall of the Moscow Con­ser­va­to­ry, Tokyo Me­t­ro­­po­l­i­­tan The­atre, Os­aka Fes­ti­val Hall, Palau de la Mú­si­ca in Barcelona, Bösendor­fer Saal in Vi­enna, Col­ston Hall in Bris­tol, Her­mitage The­atre in Saint Pe­ters­burg, Na­tional Phil­har­monic in War­saw, the Con­cert Hall of the Pol­ish Na­tional Ra­dio Sym­phony Or­ches­tra in Ka­tow­ice, and the Witold Lu­tosławski Con­cert Stu­dio in War­saw.

Górecka fre­quently par­tic­i­pates in world pre­mieres of con­­tem­po­rary works, with some pieces com­posed spe­ci­f­i­cally for her, such as Pi­ano Sonatas by Mikołaj Pi­otr Gó­rec­ki and Tomasz Kamieniak. She has been a reg­u­lar par­tic­i­pant in the In­ter­na­tional Fes­ti­val of Con­tem­po­rary Mu­sic "War­saw Au­tumn," per­form­ing works by Hen­ryk Mikołaj Gó­rec­ki, Tomasz Siko­rski, Zyg­munt Krau­ze, among oth­ers.

Aspe­cial place in Góreck­a's reper­toire holds the work of her fa­ther, Hen­ryk Mikołaj Górecki. In 2021, she served as the ed­i­tor of a mu­sic al­bum con­tain­ing his pre­vi­ously un­pub­lished works, re­leased by Boosey & Hawkes. Upon re­view­ing the publication Andrew Eales wrote: The 'Pi­ano Al­bum' is edited by the com­poser’s daugh­ter, con­cert pi­anist Anna Gó­recka, and of­fers a fas­ci­nat­ing and ap­proach­able snap­shot of his evolv­ing art. (...) Górecka pro­vides an il­lu­mi­nat­ing and ex­­haus­tive overview of the com­poser’s sub­se­quent pi­ano com­pos­ing, no doubt bring­ing the per­sonal in­sight only avail­able to so close a fam­ily mem­ber.

She re­cord­ed all of her fa­ther's pi­ano com­po­si­tions on the al­bum Anna Górecka Plays Hen­ryk Mikołaj Górecki, re­leased in 2022, which re­ceived a nom­i­na­tion for the Fry­deryk 2023 award in the "Al­bum of the Year: Solo Recital" cat­e­gory.