RCA Corp. and C.I.T. Financial Corp., who broke off merger talks a month ago, announced today that they were back at the bargaining table discussing a possible RCA takeover of the giant finance company.

When the talks were called off last month, neither company would specify a reason, but sources close to both companies said that the price RCA was willing to pay - about $62 a share - was not acceptable to C.I.T.

"Since then," one analyst noted, "nobody has been ringing their (C.I.T.'s) doorbell, so they're back to RCA to try again for a friendly merger."

At $62 a share, the deal would be worth about $1 billion.

C.I.T is the nation's larges independent finance company. Last year it had earnings of $86.5 million.

RCA is a giant communications-electronics conglomerate, that owns, among other things, the National Broadcasting Company and Hertz Corp., the car rental company.

RCA has been casting about or an acquisition in the financial services field to help stabilize its earnings. The company has nearly $500 million in cash on hand, much of it derived from a cash sale of an Alaskan communications subsidiary to Pacific Power and Light Co. last June.

C.I.T. too has a lot of cash in the bank - it sold its National Bank of North America to Great Britain's National Westminister Bank for $430 million last April.

Before rumore of the RCA-C.I.T. talks hit Wall Street in late June, C.I.T. stock was trading for about $35.75 a share. By the time the two companies confirmed they were talking merger, on July 5, C.I.T.'s price had climbed to $53.375.

It fell sharply when the talks were called off, but began rising again last Thursday. It closed at $41.375 on Thursday, $43.125 Friday and when trading was halted today, C.I.T. was valued at $44.875 a share.

RCA fell to $24.875 today, down 37.5 cents.

In a joint announcement this afternoon, RCA and C.I.T. said that there was "no assurance that any agreement will be reached," virtually the same phrasing they confirmed their merger talks last month.

C.I.T.'s assets total nearly $5 billion. Besides the large finance company, the firm also has interests in insurance, retailing and manufacturing - including greeting cards, office equipment and electrical equipment.

Last year RCA earned a record $278.4 million on sales of $6.64 billion, despite a continuing decline in profits at its NBC subsidiary. Hertz Corp. was the biggest contributor to RCA's earning's displacing NBC.

NBC's earnings have slipped because its ratings have been declining steadily for several years.